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Quasilinear elliptic equations with discontinuous coefficients

Lucio Boccardo, Giuseppe Buttazzo (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove an existence result for equations of the form { - D i ( a i j ( x , u ) D j u ) = f in Ω u H 0 1 ( Ω ) . where the coefficients a i j ( x , s ) satisfy the usual ellipticity conditions and hypotheses weaker than the continuity with respect to the variable s . Moreover, we give a counterexample which shows that the problem above may have no solution if the coefficients a i j ( x , s ) are supposed only Borel functions

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