Local properties for weak solutions of nonlocal heat equations

Abstract

In this paper, using the De Giorgi-Nash-Moser theory, we obtain an interior parabolic Holder regularity for weak solutions of nonlocal heat equations given by an integro-differential operator L-K as follows; {LKu+partial derivative tu = 0 in Omega x (-T,0] u=g in ((R-n\Omega)x(-T,0])boolean OR(Omega x{t=-T}) where g is an element of C(R(n)x[-T, 0]) boolean AND L-infinity(R(n)x(-T, 0]) boolean AND H-T(s) (R-n) and Omega subset of R-n is a bounded domain with Lipschitz boundary. In addition, we get the local boundedness of such weak solutions. (C) 2019 Elsevier Ltd. All rights reserved.