Stefano Vita
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Stefano Vita has a total of 20 co-authors. Here are the top co-authors by number of shared publications:
- Susanna Terracini
Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Torino, Italy
10 shared publications - Giorgio Tortone
Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Torino, Italy
5 shared publications - Gabriele Fioravanti
Università di Torino, Torino, Italy
4 shared publications - Alessandro Audrito
Politecnico di Torino, Torino, Italy
3 shared publications - Seongmin Jeon
Department of Mathematics Education, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
2 shared publications - Veronica Felli
Università degli Studi di Milano-Bicocca, Milano, Italy
2 shared publications
Latest Publications
- Open Access
- 17 April 2026
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 58 (5)
Boundary unique continuation in planar domains by conformal mapping
Let be a chord arc domain. We give a simple proof of the the following fact, which is commonly known to be true: a nontrivial harmonic function which vanishes continuously on a relatively open set of the boundary cannot have the norm of the gradient which vanishes on a subset of positive surface measure (arc length). This result is conjectured to be true in higher dimensions by Lin, in Lipschitz domains. Let now be a domain with Dini mean oscillations. We prove that a nontrivial harmonic function which vanishes continuously on a relatively open subset of the boundary has a finite number of critical points in . The latter improves some recent results by Kenig and Zhao. Our technique involves a conformal mapping which moves the boundary where the harmonic function vanishes into an interior nodal line of a new harmonic function, after a further reflection. Then, size estimates of the critical set, up to the boundary, of the original harmonic function can be understood in terms of estimates of the interior critical set of the new harmonic function and of the critical set, up to the boundary, of the conformal mapping.
- 17 April 2026
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 58 (5)
Open AccessBoundary unique continuation in planar domains by conformal mapping
Let be a chord arc domain. We give a simple proof of the the following fact, which is commonly known to be true: a nontrivial harmonic function which vanishes continuously on a relatively open set of the boundary cannot have the norm of the gradient which vanishes on a subset of positive surface measure (arc length). This result is conjectured to be true in higher dimensions by Lin, in Lipschitz domains. Let now be a domain with Dini mean oscillations. We prove that a nontrivial harmonic function which vanishes continuously on a relatively open subset of the boundary has a finite number of critical points in . The latter improves some recent results by Kenig and Zhao. Our technique involves a conformal mapping which moves the boundary where the harmonic function vanishes into an interior nodal line of a new harmonic function, after a further reflection. Then, size estimates of the critical set, up to the boundary, of the original harmonic function can be understood in terms of estimates of the interior critical set of the new harmonic function and of the critical set, up to the boundary, of the conformal mapping.
- 13 January 2026
- Published by Springer Nature in La Matematica
- Vol. 5 (1) , 7
Notes on Schauder Estimates by Scaling for Second Order Linear Elliptic PDEs in Divergence Form
- 13 January 2026
- Published by Springer Nature in La Matematica
- Vol. 5 (1) , 7
Notes on Schauder Estimates by Scaling for Second Order Linear Elliptic PDEs in Divergence Form
- Open Access
Regularity for elliptic equations with monomial weights
We study regularity properties for solutions to elliptic equations that are degenerate or singular along orthogonal hyperplanes. The degenerate ellipticity is carried out by a weight term which is the monomial product of different powers of the distance functions to each hyperplane; that is, given the space dimension $d\geq2$, the number of orthogonally crossing hyperplanes $1\leq n\leq d$ and the generic variable point $z=(x,y)\in\mathbb R^{d-n}\times\mathbb R^n$, then the weight is given by $ω(y)=\prod_{i=1}^ny_i^{a_i}$ with $a_i>-1$, $y_i=\mathrm{dist}(z,Σ_i)$ and $Σ_i=\{y_i=0\}$. We prove $C^{0,α}$ and $C^{1,α}$ estimates up to the corners formed by the intersections of two or more hyperplanes, for solutions of the conormal problem with variable coefficients. This is done by a regularization-approximation procedure, a blow-up argument and Liouville theorems. Finally, we provide smoothness of solutions when the equation is isotropic and homogeneous, and we show an application to Caffarelli-Kohn-Nirenberg inequalities with monomial weights.Open AccessRegularity for elliptic equations with monomial weights
We study regularity properties for solutions to elliptic equations that are degenerate or singular along orthogonal hyperplanes. The degenerate ellipticity is carried out by a weight term which is the monomial product of different powers of the distance functions to each hyperplane; that is, given the space dimension $d\geq2$, the number of orthogonally crossing hyperplanes $1\leq n\leq d$ and the generic variable point $z=(x,y)\in\mathbb R^{d-n}\times\mathbb R^n$, then the weight is given by $ω(y)=\prod_{i=1}^ny_i^{a_i}$ with $a_i>-1$, $y_i=\mathrm{dist}(z,Σ_i)$ and $Σ_i=\{y_i=0\}$. We prove $C^{0,α}$ and $C^{1,α}$ estimates up to the corners formed by the intersections of two or more hyperplanes, for solutions of the conormal problem with variable coefficients. This is done by a regularization-approximation procedure, a blow-up argument and Liouville theorems. Finally, we provide smoothness of solutions when the equation is isotropic and homogeneous, and we show an application to Caffarelli-Kohn-Nirenberg inequalities with monomial weights. - Open Access
A priori Hölder estimates for equations degenerating on nodal sets
We prove a priori Hölder bounds for continuous solutions to degenerate equations with variable coefficients of type $$ \mathrm{div}\left(u^2 A\nabla w\right)=0\quad\mathrm{in \ }Ω\subset\mathbb R^n,\qquad \mbox{with}\qquad \mathrm{div}\left(A\nabla u\right)=0, $$ where $A$ is a Lipschitz continuous, uniformly elliptic matrix (possibly $u$ has non-trivial singular nodal set). Such estimates are uniform with respect to $u$ in a class of normalized solutions that have a bounded Almgren frequency. As a consequence, a boundary Harnack principle holds for the quotient of two solutions vanishing on a common set. This analysis relies on a detailed study of the associated weighted Sobolev spaces, including integrability of the weight, capacitary properties of the nodal set, and uniform Sobolev inequalities yielding local boundedness of solutions.Open AccessA priori Hölder estimates for equations degenerating on nodal sets
We prove a priori Hölder bounds for continuous solutions to degenerate equations with variable coefficients of type $$ \mathrm{div}\left(u^2 A\nabla w\right)=0\quad\mathrm{in \ }Ω\subset\mathbb R^n,\qquad \mbox{with}\qquad \mathrm{div}\left(A\nabla u\right)=0, $$ where $A$ is a Lipschitz continuous, uniformly elliptic matrix (possibly $u$ has non-trivial singular nodal set). Such estimates are uniform with respect to $u$ in a class of normalized solutions that have a bounded Almgren frequency. As a consequence, a boundary Harnack principle holds for the quotient of two solutions vanishing on a common set. This analysis relies on a detailed study of the associated weighted Sobolev spaces, including integrability of the weight, capacitary properties of the nodal set, and uniform Sobolev inequalities yielding local boundedness of solutions. - Open Access
- 15 April 2025
- Published by European Mathematical Society - EMS - Publishing House GmbH in Revista Matemática Iberoamericana
- Vol. 41 (4) , 1513-1554
Higher order Schauder estimates for degenerate or singular parabolic equations
In this paper, we complete the analysis initiated in [Calc. Var. Partial Differential Equations 63 (2024), article no. 204] establishing some higher order C^{k+2,\alpha} Schauder estimates ( k \in \mathbb{N} ) for a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The C^{2,\alpha} -estimates are obtained through a blow-up argument and a Liouville theorem, while the higher order estimates are obtained by a fine iteration procedure. As a byproduct, we present two applications. First, we prove similar Schauder estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type. Second, we provide an alternative proof of the higher order boundary Harnack principles established in [J. Differential Equations 260 (2016), 1801–1829] and [Discrete Contin. Dyn. Syst. 42 (2022), 2667–2698].
- 15 April 2025
- Published by European Mathematical Society - EMS - Publishing House GmbH in Revista Matemática Iberoamericana
- Vol. 41 (4) , 1513-1554
Open AccessHigher order Schauder estimates for degenerate or singular parabolic equations
In this paper, we complete the analysis initiated in [Calc. Var. Partial Differential Equations 63 (2024), article no. 204] establishing some higher order C^{k+2,\alpha} Schauder estimates ( k \in \mathbb{N} ) for a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The C^{2,\alpha} -estimates are obtained through a blow-up argument and a Liouville theorem, while the higher order estimates are obtained by a fine iteration procedure. As a byproduct, we present two applications. First, we prove similar Schauder estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type. Second, we provide an alternative proof of the higher order boundary Harnack principles established in [J. Differential Equations 260 (2016), 1801–1829] and [Discrete Contin. Dyn. Syst. 42 (2022), 2667–2698].
- 7 November 2024
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 63 (9) , 1-42
Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients
- 7 November 2024
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 63 (9) , 1-42
Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients
- 4 September 2024
- Published by Elsevier in Journal of Differential Equations
- Vol. 412, 808-856
Higher order boundary Harnack principles in Dini type domains
- 4 September 2024
- Published by Elsevier in Journal of Differential Equations
- Vol. 412, 808-856
Higher order boundary Harnack principles in Dini type domains
- Open Access
- 20 August 2024
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 63 (8) , 1-46
Schauder estimates for parabolic equations with degenerate or singular weights
We establish some $$C^{0,\alpha }$$ and $$C^{1,\alpha }$$ regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or explode on a characteristic hyperplane $$\Sigma $$ as a power $$a > -1$$ of the distance to $$\Sigma $$ . The estimates we obtain are sharp with respect to the assumptions on coefficients and data. Our methods rely on a regularization of the equation and some uniform regularity estimates combined with a Liouville theorem and an approximation argument. As a corollary of our main result, we obtain similar $$C^{1,\alpha }$$ estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type.- 20 August 2024
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 63 (8) , 1-46
Open AccessSchauder estimates for parabolic equations with degenerate or singular weights
We establish some $$C^{0,\alpha }$$ and $$C^{1,\alpha }$$ regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or explode on a characteristic hyperplane $$\Sigma $$ as a power $$a > -1$$ of the distance to $$\Sigma $$ . The estimates we obtain are sharp with respect to the assumptions on coefficients and data. Our methods rely on a regularization of the equation and some uniform regularity estimates combined with a Liouville theorem and an approximation argument. As a corollary of our main result, we obtain similar $$C^{1,\alpha }$$ estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type. - Open Access
Unique continuation from conical boundary points for fractional equations
We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev type inequality. Then, the asymptotics of solutions at the conical point follow by an Almgren type monotonicity formula, blow-up analysis and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary.
Open AccessUnique continuation from conical boundary points for fractional equations
We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev type inequality. Then, the asymptotics of solutions at the conical point follow by an Almgren type monotonicity formula, blow-up analysis and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary.
- Top Cited Papers
- 29 March 2024
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 248 (2) , 1-44
Higher Order Boundary Harnack Principle via Degenerate Equations
- 29 March 2024
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 248 (2) , 1-44
Top Cited PapersHigher Order Boundary Harnack Principle via Degenerate Equations