On Some regularity properties for solutions of nonlinear parabolic differential equations
Haruo Nagase · Nagoya Mathematical Journal · 1992
Let G be a bounded domain in Rn with coordinates x = (x1,…,xn) and let its boundary S be of class C2. We assume that the usual function spaces Lq(G), Wl, q(G) and are known. We write the norm of Lq(G) by | |q and the adjoint number of q by q*, i.e., q* = q/(q —1). For any positive number T we denote the open interval (0,T) by I, the cylinder G X I in Rn+1 by Q and the norm of Lq(Q) by ‖ ‖q.