Abstract
We study a class of Dirichlet boundary value problems whose prototype is
[see formula in PDF]
where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on [see formula in PDF] whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
Funder
INdAM-GNAMPA
Spanish Ministerio de Ciencia, Innovaci´on y Universidades and FEDER
MIUR-PRIN 2017 “Direct and inverse problems for partial differential equations: theoretical aspects and applications
Università della Campania "L.Vanvitelli" - VAIN-HOPES: “VArIational methods and Numerical techniques: sHape Optimization and nonlinear Partial differential EquationS”
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Cited by
2 articles.
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