Local properties for weak solutions of nonlocal heat equations. (March 2020) - Kim, Yong-Cheol
Abstract: In this paper, using the De Giorgi–Nash–Moser theory, we obtain an interior parabolic Hölder regularity for weak solutions of nonlocal heat equations given by an integro-differential operator L K as follows; L K u + ∂ t u = 0 in Ω × ( − T, 0 ] u = g in ( ( R n ∖ Ω ) × ( − T, 0 ] ) ∪ ( Ω × t = − T ) where g ∈ C ( R n × [ − T, 0 ] ) ∩ L ∞ ( R n × ( − T, 0 ] ) ∩ H T s ( R n ) and Ω ⊂ R n is a bounded domain with Lipschitz boundary. In addition, we get the local boundedness of such weak solutions.