On the Problem of Maximal $L^q$-regularity for Viscous Hamilton–Jacobi Equations
Open Access
- 30 March 2021
- journal article
- research article
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 240 (3) , 1521-1534
Abstract
In this paper we prove a conjecture by P.-L. Lions on maximal regularity of $$L^q$$ -type for periodic solutions to $$-\Delta u + |Du|^\gamma = f$$ in $$\mathbb {R}^d$$ , under the (sharp) assumption that $$q > d \frac{\gamma -1}{\gamma }$$ .
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- Università degli Studi di Padova
This publication has 30 references indexed in Scilit:
- Existence and a priori estimate for elliptic problems with subquadratic gradient dependent termsComptes Rendus Mathematique, 2005
- Existence results for a class of nonlinear elliptic problems with p-growth in the gradientNonlinear Analysis, 2003
- Nonlinear elliptic equations with natural growth in general domainsAnnali di Matematica Pura ed Applicata (1923 -), 2002
- On ergodic stochastic controlCommunications in Partial Differential Equations, 1998
- Nonlinear degenerate elliptic partial differential equations with critical growth conditions on the gradientProceedings of the American Mathematical Society, 1995
- Weak Solutions of Some Quasilinear Elliptic Equations with Data MeasuresSIAM Journal on Mathematical Analysis, 1993
- $L^\infty $ Estimate for Some Nonlinear Elliptic Partial Differential Equations and Application to an Existence ResultSIAM Journal on Mathematical Analysis, 1992
- Viscosity solutions of fully nonlinear second-order elliptic partial differential equationsJournal of Differential Equations, 1990
- Universality classes for deterministic surface growthPhysical Review A, 1988
- The problem of dirichlet for quasilinear elliptic differential equations with many independent variablesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1969