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Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I

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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.

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Authors
  1. S. Bonafede
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Bonafede, S. Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I. Ukr Math J 48, 977–987 (1996). https://doi.org/10.1007/BF02390956

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  • DOI: https://doi.org/10.1007/BF02390956

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