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Elliptic equations and differential inclusions. (English) Zbl 0891.35034

Summary: The aim of the present paper is to show that some questions concerning elliptic differential equations may profitably be investigated by using techniques and results from set-valued analysis. Precisely, we briefly discuss the following topics:
1) Elliptic problems having nonlinear terms discontinuous at a set of points of Lebesgue measure zero only.
2) Implicit elliptic equations.
3) Elliptic eigenvalue problems with highly discontinuous nonlinearities.

MSC:

35J60 Nonlinear elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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