Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774355 | Journal of Differential Equations | 2017 | 132 Pages |
Abstract
We consider parabolic operators of the formât+L,L=âdivA(X,t)â, in R+n+2:={(X,t)=(x,xn+1,t)âRnÃRÃR:xn+1>0}, nâ¥1. We assume that A is a (n+1)Ã(n+1)-dimensional matrix which is bounded, measurable, uniformly elliptic and complex, and we assume, in addition, that the entries of A are independent of the spatial coordinate xn+1 as well as of the time coordinate t. For such operators we prove that the boundedness and invertibility of the corresponding layer potential operators are stable on L2(Rn+1,C)=L2(âR+n+2,C) under complex, Lâ perturbations of the coefficient matrix. Subsequently, using this general result, we establish solvability of the Dirichlet, Neumann and Regularity problems for ât+L, by way of layer potentials and with data in L2, assuming that the coefficient matrix is a small complex perturbation of either a constant matrix or of a real and symmetric matrix.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Kaj Nyström,