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Generalized nonlocal Robin Laplacian on arbitrary domains View Full Text

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Article Info

DATE

2021-10-13

AUTHORS

Nouhayla Ait Oussaid, Khalid Akhlil, Sultana Ben Aadi, Mourad El Ouali

ABSTRACT

In this paper, we prove that it is always possible to define a realization of the Laplacian Δκ,θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _{\kappa ,\theta }$$\end{document} on L2(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2(\Omega )$$\end{document} subject to nonlocal Robin boundary conditions with general jump measures on arbitrary open subsets of RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^N$$\end{document}. This is made possible by using a capacity approach to define an admissible pair of measures (κ,θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\kappa ,\theta )$$\end{document} that allows the associated form Eκ,θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {E}}_{\kappa ,\theta }$$\end{document} to be closable. The nonlocal Robin Laplacian Δκ,θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _{\kappa ,\theta }$$\end{document} generates a sub-Markovian C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0$$\end{document}-semigroup on L2(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2(\Omega )$$\end{document} which is not dominated by the Neumann Laplacian semigroup unless the jump measure θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} vanishes. More... »

PAGES

675-686

References to SciGraph publications

  • 2020-03-14. Realization of the fractional Laplacian with nonlocal exterior conditions via forms method in JOURNAL OF EVOLUTION EQUATIONS
  • 2003-02. Dirichlet and Neumann boundary conditions: What is in between? in JOURNAL OF EVOLUTION EQUATIONS
  • 1993-06. Closability and resolvent of Dirichlet forms perturbed by jumps in POTENTIAL ANALYSIS
  • 1996-12. Invariance of closed convex sets and domination criteria for semigroups in POTENTIAL ANALYSIS
  • 2018-04-06. Locality and Domination of Semigroups in RESULTS IN MATHEMATICS
  • 2003-12. The Laplacian with Robin Boundary Conditions on Arbitrary Domains in POTENTIAL ANALYSIS

    • Journal

    TITLE

    Archiv der Mathematik

    ISSUE

    6

    VOLUME

    117

    Subjects

  • FOR: Mathematical Sciences
  • FOR: Pure Mathematics

    • Author Affiliations

  • Departement of Mathematics and Management, Polydisciplinary Faculty of Ouarzazate, Ibno Zohr University, Agadir, Morocco
  • Research Group Discrete Optimization, Department of Computer Science, CAU Kiel, Kiel, Germany

    • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00013-021-01663-4

    DOI

    http://dx.doi.org/10.1007/s00013-021-01663-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1141849660

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