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Elliptic boundary-value problems with discontinuous nonlinearities. (English) Zbl 0843.35034

The author studies existence of weak solutions of semilinear elliptic equations with discontinuous nonlinearities. The abstract framework is the one of analysis of set-valued mappings. Nonlinearities having a set of discontinuities with Lebesgue measure zero and which in some sense are below the first eigenvalue of the Laplace operator under Dirichlet boundary conditions are treated. The author also gets some estimates on the Laplacian of the solutions.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35R70 PDEs with multivalued right-hand sides
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