Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I

  • S. Bonafede

Abstract

This paper is concerned with the existence and uniqueness of variational solutions of the strongly nonlinear equation $$ - \sum\limits_1^m {_i \frac{\partial }{{\partial x_i }}\left( {\sum\limits_1^m {_j a_{i,j} (x, u(x))\frac{{\partial u(x)}}{{\partial x_j }}} } \right) + g(x, u(x)) = f(x)} $$ with the coefficients a i,j (x, s) satisfying an eHipticity degenerate condition and hypotheses weaker than the continuity with respect to the variable s. Furthermore, we establish a condition on f under which the solution is bounded in a bounded open subset Ω of Rm.
Published
25.07.1996
How to Cite
BonafedeS. “Strongly Nonlinear Degenerate Elliptic Equations With Discontinuous Coefficients. I”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 7, July 1996, pp. 867-75, https://umj.imath.kiev.ua/index.php/umj/article/view/5259.
Section
Research articles