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...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00217824_v105_n6_p810_Mazon |
| Aporte de: |
| id |
todo:paper_00217824_v105_n6_p810_Mazon |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00217824_v105_n6_p810_Mazon2023-10-03T14:20:49Z Fractional p-Laplacian evolution equations Mazón, J.M. Rossi, J.D. Toledo, J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Mazón, J.M. Rossi, J.D. Toledo, J. 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. |
| format |
JOUR |
| author |
Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_facet |
Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_sort |
Mazón, J.M. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00217824_v105_n6_p810_Mazon |
| work_keys_str_mv |
AT mazonjm fractionalplaplacianevolutionequations AT rossijd fractionalplaplacianevolutionequations AT toledoj fractionalplaplacianevolutionequations |
| _version_ |
1807318379878416384 |