L^p regularity, heat equation



Just wondering if anyone knows the L^p regularity theory for

u_t (x,t)-Delta u(x,t) = f(x,t) in Omega x (0,T)

u(x,0)=0

u(x,t)=0 on side of cylinder


and where $ f \in L^p(0,T;L^q(Omega))$.


Here Omega is bounded nice...


thanks


craig
.



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