TY - JOUR
AU1 - Oussaid, Nouhayla Ait
AU2 - Akhlil, Khalid
AU3 - Aadi, Sultana Ben
AU4 - Ouali, Mourad El
AB - 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.
TI - Generalized nonlocal Robin Laplacian on arbitrary domains
JF - Archiv der Mathematik
DO - 10.1007/s00013-021-01663-4
DA - 2021-12-01
UR - https://www.deepdyve.com/lp/springer-journals/generalized-nonlocal-robin-laplacian-on-arbitrary-domains-QzcU1bjIF8
SP - 675
EP - 686
VL - 117
IS - 6
DP - DeepDyve
ER -