Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions
In this paper we study existence and uniqueness of solutions to the local diffusion equation with Neumann boundary conditions and a bounded nonhomogeneous diffusion coefficient g ≥ 0, {ut = div (g|∇u|p-2∇u) in ]0; T[×Ωg|∇u|p-2u·n = 0 on ]0; T[×∂Ω; for 1 ≤ p < ∞. We show that a nonlocal counte...
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todo:paper_02141493_v55_n1_p27_Andreu2023-10-03T15:10:12Z Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions Andreu, F. Mazón, J.M. Rossi, J.D. Toledo, J. Neumann boundary conditions Nonlocal diffusion P-Laplacian Total variation ow In this paper we study existence and uniqueness of solutions to the local diffusion equation with Neumann boundary conditions and a bounded nonhomogeneous diffusion coefficient g ≥ 0, {ut = div (g|∇u|p-2∇u) in ]0; T[×Ωg|∇u|p-2u·n = 0 on ]0; T[×∂Ω; for 1 ≤ p < ∞. We show that a nonlocal counterpart of this diffusion problem is ut(t; x)= ∫ω J(x-y)g(x+y/2)|u(t; y)-u(t; x)| p-2 (u(t; y)-u(t; x)) dy in ]0; T[× Ω,where the diffusion coefficient has been reinterpreted by means of the values of g at the point x+y/2 in the integral operator. The fact that g ≥ 0 is allowed to vanish in a set of positive measure involves subtle difficulties, specially in the case p = 1. 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_02141493_v55_n1_p27_Andreu |
| institution |
Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Neumann boundary conditions Nonlocal diffusion P-Laplacian Total variation ow |
| spellingShingle |
Neumann boundary conditions Nonlocal diffusion P-Laplacian Total variation ow Andreu, F. Mazón, J.M. Rossi, J.D. Toledo, J. Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions |
| topic_facet |
Neumann boundary conditions Nonlocal diffusion P-Laplacian Total variation ow |
| description |
In this paper we study existence and uniqueness of solutions to the local diffusion equation with Neumann boundary conditions and a bounded nonhomogeneous diffusion coefficient g ≥ 0, {ut = div (g|∇u|p-2∇u) in ]0; T[×Ωg|∇u|p-2u·n = 0 on ]0; T[×∂Ω; for 1 ≤ p < ∞. We show that a nonlocal counterpart of this diffusion problem is ut(t; x)= ∫ω J(x-y)g(x+y/2)|u(t; y)-u(t; x)| p-2 (u(t; y)-u(t; x)) dy in ]0; T[× Ω,where the diffusion coefficient has been reinterpreted by means of the values of g at the point x+y/2 in the integral operator. The fact that g ≥ 0 is allowed to vanish in a set of positive measure involves subtle difficulties, specially in the case p = 1. |
| format |
JOUR |
| author |
Andreu, F. Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_facet |
Andreu, F. Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_sort |
Andreu, F. |
| title |
Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions |
| title_short |
Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions |
| title_full |
Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions |
| title_fullStr |
Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions |
| title_full_unstemmed |
Local and nonlocal weighted p-laplacian evolution equations with Neumann boundary conditions |
| title_sort |
local and nonlocal weighted p-laplacian evolution equations with neumann boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_02141493_v55_n1_p27_Andreu |
| work_keys_str_mv |
AT andreuf localandnonlocalweightedplaplacianevolutionequationswithneumannboundaryconditions AT mazonjm localandnonlocalweightedplaplacianevolutionequationswithneumannboundaryconditions AT rossijd localandnonlocalweightedplaplacianevolutionequationswithneumannboundaryconditions AT toledoj localandnonlocalweightedplaplacianevolutionequationswithneumannboundaryconditions |
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1782029937772855296 |