Search results for "1-Laplacian"

showing 4 items of 4 documents

Elliptic problems involving the 1–Laplacian and a singular lower order term

2018

General Mathematics010102 general mathematicsLower orderelliptic problems1-Laplacian01 natural sciencesTerm (time)010101 applied mathematicssingular lower order termsApplied mathematics0101 mathematicsLaplace operator1-Laplacian; singular lower order terms; elliptic problemsMathematicsJournal of the London Mathematical Society
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Bounded solutions to the 1-Laplacian equation with a critical gradient term

2012

General MathematicsBounded functionMathematical analysisLaplace operator1-laplacian; degenerate elliptic equations; functions of bounded variations; gradient term with natural growthMathematicsTerm (time)Asymptotic Analysis
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Multiplicity of Solutions to Elliptic Problems Involving the 1-Laplacian with a Critical Gradient Term

2017

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.

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 operatorMathematicsAdvanced Nonlinear Studies
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Dimension reduction for $-Delta_1$

2012

A 3D-2D dimension reduction for $-\Delta_1$ is obtained. A power law approximation from $-\Delta_p$ as $p \to 1$ in terms of $\Gamma$- convergence, duality and asymptotics for least gradient functions has also been provided.

dimension reduction; gamma convergence; duality; functions of bounded variation; 1-laplacianMathematics - Analysis of PDEsdimension reductionfunctions of bounded variationdualitygamma convergence1-laplacian
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