Fractional p-Laplacian evolution equations

In this paper we study the fractional p-Laplacian evolution equation given by. ut(t,x)=∫A1/|x-y|N+sp|u(t,y)-u(t,x)|p-2(u(t,y)-u(t,x))dy for x∈Ω, t>0, 0 < s< 1, p≥ 1. In a bounded domain Ω we deal with the Dirichlet problem by taking A = RN and u= 0 in RN\\Ω, and the Neumann prob...

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Autor principal: Rossi, Julio Daniel
Publicado: 2016
Materias:
Cauchy problem
Dirichlet problem
Fractional Sobolev spaces
Neumann problem
P-Laplacian
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v105_n6_p810_Mazon
http://hdl.handle.net/20.500.12110/paper_00217824_v105_n6_p810_Mazon
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00217824_v105_n6_p810_Mazon
record_format dspace
spelling paper:paper_00217824_v105_n6_p810_Mazon2023-06-08T14:42:04Z Fractional p-Laplacian evolution equations Rossi, Julio Daniel Cauchy problem Dirichlet problem Fractional Sobolev spaces Neumann problem P-Laplacian In this paper we study the fractional p-Laplacian evolution equation given by. ut(t,x)=∫A1/|x-y|N+sp|u(t,y)-u(t,x)|p-2(u(t,y)-u(t,x))dy for x∈Ω, t>0, 0 < s< 1, p≥ 1. In a bounded domain Ω we deal with the Dirichlet problem by taking A = RN and u= 0 in RN\\Ω, and the Neumann problem by taking A=. Ω. We include here the limit case p= 1 that has the extra difficulty of giving a meaning to u(y)-u(x)|u(y)-u(x)| when u( y) = u( x). We also consider the Cauchy problem in the whole RN by taking A=Ω=RN. We find existence and uniqueness of strong solutions for each of the above mentioned problems. We also study the asymptotic behaviour of these solutions as t→∞. Finally, we recover the local p-Laplacian evolution equation with Dirichlet or Neumann boundary conditions, and for the Cauchy problem, by taking the limit as s→1 in the nonlocal problems multiplied by a suitable scaling constant. © 2016 Elsevier Masson SAS. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v105_n6_p810_Mazon http://hdl.handle.net/20.500.12110/paper_00217824_v105_n6_p810_Mazon
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cauchy problem
Dirichlet problem
Fractional Sobolev spaces
Neumann problem
P-Laplacian
spellingShingle Cauchy problem
Dirichlet problem
Fractional Sobolev spaces
Neumann problem
P-Laplacian
Rossi, Julio Daniel
Fractional p-Laplacian evolution equations
topic_facet Cauchy problem
Dirichlet problem
Fractional Sobolev spaces
Neumann problem
P-Laplacian
description In this paper we study the fractional p-Laplacian evolution equation given by. ut(t,x)=∫A1/|x-y|N+sp|u(t,y)-u(t,x)|p-2(u(t,y)-u(t,x))dy for x∈Ω, t>0, 0 < s< 1, p≥ 1. In a bounded domain Ω we deal with the Dirichlet problem by taking A = RN and u= 0 in RN\\Ω, and the Neumann problem by taking A=. Ω. We include here the limit case p= 1 that has the extra difficulty of giving a meaning to u(y)-u(x)|u(y)-u(x)| when u( y) = u( x). We also consider the Cauchy problem in the whole RN by taking A=Ω=RN. We find existence and uniqueness of strong solutions for each of the above mentioned problems. We also study the asymptotic behaviour of these solutions as t→∞. Finally, we recover the local p-Laplacian evolution equation with Dirichlet or Neumann boundary conditions, and for the Cauchy problem, by taking the limit as s→1 in the nonlocal problems multiplied by a suitable scaling constant. © 2016 Elsevier Masson SAS.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Fractional p-Laplacian evolution equations
title_short Fractional p-Laplacian evolution equations
title_full Fractional p-Laplacian evolution equations
title_fullStr Fractional p-Laplacian evolution equations
title_full_unstemmed Fractional p-Laplacian evolution equations
title_sort fractional p-laplacian evolution equations
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v105_n6_p810_Mazon
http://hdl.handle.net/20.500.12110/paper_00217824_v105_n6_p810_Mazon
work_keys_str_mv AT rossijuliodaniel fractionalplaplacianevolutionequations
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