LOCAL AND NONLOCAL WEIGHTED p-LAPLACIAN EVOLUTION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

被引：25

作者：

Andreu, F. ^{[1
]}

Mazon, J. M. ^{[1
]}

Rossi, J. D. ^{[2
]}

Toledo, J. ^{[1
]}

机构：

[1] Univ Valencia, Dept Anal Matemat, Valencia, Spain

[2] FCEyN UBA 1428, Dept Matemat, Buenos Aires, DF, Argentina

来源：

PUBLICACIONS MATEMATIQUES | 2011年 / 55卷 / 01期

关键词：

Nonlocal diffusion; p-Laplacian; total variation flow; Neumann boundary conditions; CONVOLUTION MODEL; OBSTACLE PROBLEM; REGULARITY; DISPERSAL; STABILITY;

D O I：

10.5565/PUBLMAT_55111_03

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, {u(t) = div (g vertical bar del u vertical bar(p-2)del u) in ]0,T[x Omega, g vertical bar del u vertical bar(p-2)del u . eta = 0 on ]0,T[x partial derivative Omega, for 1 <= p < infinity. We show that a nonlocal counterpart of this diffusion problem is u(t)(t,x) = integral(Omega)J(x-y)g(x+y/2)vertical bar u(t,y)-u(t,x)vertical bar(p-2)(u(t,y)-u(t,x)) dy in ]0,T[x Omega, 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.

引用

页码：27 / 66

页数：40

共 51 条

[1] A NOTION OF TOTAL VARIATION DEPENDING ON A METRIC WITH DISCONTINUOUS COEFFICIENTS [J].