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RESEARCH PRODUCT

Multiplicity of Solutions to Elliptic Problems Involving the 1-Laplacian with a Critical Gradient Term

Sergio Segura De LeónBoumediene AbdellaouiAndrea Dall'aglio

subject

Pure mathematicsboundary-value problemsGeneral Mathematics010102 general mathematicsStatistical and Nonlinear PhysicsMultiplicity (mathematics)Partial differential equations; 1-Laplacian; multiplicity; boundary-value problemsPartial differential equations1-Laplacian01 natural sciences010101 applied mathematicsmultiplicity0101 mathematicsLaplace operatorMathematics

description

Abstract In the present paper we study the Dirichlet problem for an equation involving the 1-Laplacian and a total variation term as reaction.We prove a strong multiplicity result. Namely, we show that for any positive Radon measure concentrated in a set away from the boundary and singular with respect to a certain capacity, there exists an unbounded solution, and measures supported on disjoint sets generate different solutions.These results can be viewed as the analogue for the 1-Laplacian operator of some known multiplicity results which were first obtained by Ireneo Peral, to whom this article is dedicated, and his collaborators.

yearjournalcountryeditionlanguage
2017-04-21Advanced Nonlinear Studies
https://doi.org/10.1515/ans-2017-0011