In this Note we consider a class of noncoercive nonlinear problems whose prototype is -Delta(p)u + b(x)\delu\(lambda) = mu in Omega, u = 0 on partial derivativeOmega where Q is a bounded open subset of R-N (N greater than or equal to 2), Delta(p) is the so called p-Laplace operator (1 < p < N) or a variant of it, g is a Radon measure with bounded variation on 2 or a function in L-1 (Omega), lambda greater than or equal to 0 and b belongs to the Lorentz space L-N,L-1 (Omega) or to the Lebesgue space L-infinity(Omega). We prove existence and uniqueness of renormalized solutions.
Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum / M. F., Betta; Mercaldo, Anna; F., Murat; M. M., Porzio. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - STAMPA. - 334:9(2002), pp. 757-762. [10.1016/S1631-073X(02)02338-5]
Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum
MERCALDO, ANNA;
2002
Abstract
In this Note we consider a class of noncoercive nonlinear problems whose prototype is -Delta(p)u + b(x)\delu\(lambda) = mu in Omega, u = 0 on partial derivativeOmega where Q is a bounded open subset of R-N (N greater than or equal to 2), Delta(p) is the so called p-Laplace operator (1 < p < N) or a variant of it, g is a Radon measure with bounded variation on 2 or a function in L-1 (Omega), lambda greater than or equal to 0 and b belongs to the Lorentz space L-N,L-1 (Omega) or to the Lebesgue space L-infinity(Omega). We prove existence and uniqueness of renormalized solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
