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Uniqueness of solutions for some nonlinear Dirichlet problems

Authors:

Email author" target="_blank">Alessio?Porretta Email author

Institution:

(1) Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133 Roma, Italy

Abstract:

We consider here a class of nonlinear Dirichlet problems, in a bounded domain OHgr

, of the form

$\left\{ {\begin{array}{*{20}l} { - {\text{div}}(a(x,u)\nabla u) + {\text{div}}(\Phi (u)) = f{\text{ in }}\Omega ,} \\ {u = 0\quad {\text{on }}\partial \Omega ,} \\ \end{array} } \right.$

investigating the problem of uniqueness of solutions. The functions PHgr

(s) and $s \mapsto a(x,s)$ satisfy rather general assumptions of locally Lipschitz continuity (with possibly exponential growth) and the datum f is in L¹( OHgr

). Uniqueness of solutions is proved both for coercive a(x, s) and for the case of a(x, s) degenerating for s large.

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35J60 (35J65 35R05)

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