Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data

Dall’Aglio, Andrea; León, Sergio Segura de

doi:10.21136/cmj.2018.0322-17

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“…Recall that, on account of our hypothesis dist(A, ∂Ω) > , we may apply [13,Theorem 4.3] and deduce that each solution u p is bounded in any closed subset of Ω \ A. Let B R denote a ball of radius R > such that B R ∩ A = and |B R | < .…”

Section: It Is Straightforward That Thenmentioning

confidence: 99%

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

Abdellaoui

Dall’Aglio

León

2017

Advanced Nonlinear Studies

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In the present paper we study the Dirichlet problem for an equation involving the -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 -Laplacian operator of some known multiplicity results which were first obtained by Ireneo Peral, to whom this article is dedicated, and his collaborators.

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Section: It Is Straightforward That Thenmentioning

confidence: 99%

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

Abdellaoui

Dall’Aglio

León

2017

Advanced Nonlinear Studies

Self Cite

View full text Add to dashboard Cite

show abstract

Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data

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Cited by 1 publication

References 10 publications

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

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

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