A Remark on Bony Maximum Principle
- 1 July 1983
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 88 (3), 503-508
- https://doi.org/10.2307/2045002
Abstract
We extend a result due to J. M. Bony concerning a form of the classical maximum principle adapted to Sobolev spaces. We treat the case of the limiting exponent and show that the result is optimal. We give various applications to nonlinear elliptic partial differential equations.Keywords
This publication has 9 references indexed in Scilit:
- An Introduction to Variational Inequalities and Their ApplicationsPublished by Society for Industrial & Applied Mathematics (SIAM) ,2000
- Some Properties of Viscosity Solutions of Hamilton-Jacobi EquationsTransactions of the American Mathematical Society, 1984
- Viscosity Solutions of Hamilton-Jacobi EquationsTransactions of the American Mathematical Society, 1983
- Optimal stochastic control of diffusion type processes and Hamilton-Jacobi-Bellman equationsPublished by Springer Nature ,1982
- Resolution analytique des problemes de Bellman-DirichletActa Mathematica, 1981
- Controlled Diffusion ProcessesPublished by Springer Nature ,1980
- Elliptic (second-order) partial differential equations with measurable coefficients and approximating integral equationsAdvances in Mathematics, 1976
- On the smoothness of superharmonics which solve a minimum problemJournal d'Analyse Mathématique, 1970
- Limitazioni per soluzioni di equazioni ellitticheAnnali di Matematica Pura ed Applicata (1923 -), 1966