We consider a class of nonlinear elliptic equations containing a -Laplacian type operator, lower order terms having natural growth with respect to the gradient, and bounded measures as data. The model example is the equation
in a bounded set , coupled with a Dirichlet boundary condition. We provide a review of the results recently obtained in the absorption case (when ) and prove a new existence result without any sign condition on , assuming only that . This latter assumption is proved to be optimal for existence of solutions for any measure .
Published December 28, 2002.
Subject classfications: 35J60, 35J65, 35R05.
Key words: Nonlinear elliptic equations, natural growth terms, measure data.
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|Alessio Porretta |
Dipartimento di Matematica,
Universita di Roma "Tor Vergata",
Via della Ricerca Scientifica 1,
00133, Roma, Italia.
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