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Continuity of solutions for the Δϕ-Laplacian operator

Part of: Existence theories Miscellaneous topics - Partial differential equations Linear function spaces and their duals Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  11 September 2020

Natalí A. Cantizano ,
Ariel M. Salort  and
Juan F. Spedaletti
Natalí A. Cantizano
Affiliation:
Departamento de Matemática, FCFMyN, Universidad Nacional de San Luis, Instituto de Matemática Aplicada San Luis, IMASL, CONICET, Italia avenue 1556, San Luis 5700, San Luis, Argentina ([email protected])
Ariel M. Salort
Affiliation:
Departamento de Matemática FCEyN, Universidad de Buenos Aires and IMAS – CONICET, Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina ([email protected])
Juan F. Spedaletti
Affiliation:
Departamento de Matemática, FCFMyN, Universidad Nacional de San Luis, Instituto de Matemática Aplicada San Luis, IMASL, CONICET, Italia avenue 1556, office 155, San Luis 5700, San Luis, Argentina ([email protected])
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Abstract

In this paper we give sufficient conditions to obtain continuity results of solutions for the so called ϕ-Laplacian Δϕ with respect to domain perturbations. We point out that this kind of results can be extended to a more general class of operators including, for instance, nonlocal nonstandard growth type operators.

Keywords

Orlicz–Sobolevnonstandard growth

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 35R99: None of the above, but in this section 35R11: Fractional partial differential equations 35P99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 4 , August 2021 , pp. 1355 - 1382
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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