6533b82efe1ef96bd1293468

RESEARCH PRODUCT

A singular elliptic equation and a related functional

Sergio Segura De LeónA. FeroneAnna Mercaldo

subject

0209 industrial biotechnologyPure mathematicsControl and OptimizationSemilinear equation010102 general mathematicsSingular termExistence02 engineering and technologyType (model theory)01 natural sciencesDirichlet distributionComputational MathematicsElliptic curvesymbols.namesake020901 industrial engineering & automationControl and Systems EngineeringsymbolsStandard probability spaceBoundary value problemUniquenessSingularity at u = 0Uniqueness0101 mathematicsMathematicsSign (mathematics)

description

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.

yearjournalcountryeditionlanguage
2021-01-01
10.1051/cocv/2021037https://hdl.handle.net/11591/460672