Publication: On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
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Cambridge Univ Press
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Abstract
In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.
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Keywords
1-Laplacian operator, space of functions of bounded variation, discontinuous nonlinearities
Language
English
Citation
Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 27 p., 2022.
