An upper estimate of solution for a general class of parabolic equations
An upper estimate of solution for a general class of parabolic equations
The authors prove an estimate on the \(L^\infty\) norm of solutions of parabolic differential equations in divergence form. Such estimates are well known [see, for example, \textit{D. G. Aronson} and \textit{J. Serrin}, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 21, 291-305 (1967; Zbl 0148.34803)] for power nonlinearities. The new ingredient here is the consideration of nonpower laws such as in the reviewer's paper [Commun. Partial Differ. Equations 16, 311-361 (1991; Zbl 0742.35028)].
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, estimate on the \(L^\infty\) norm, integro-differential inequalities, A priori estimates in context of PDEs
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, estimate on the \(L^\infty\) norm, integro-differential inequalities, A priori estimates in context of PDEs