zbMATH — the first resource for mathematics

Parabolic boundary value problems on a nonsmooth domain. (Problèmes aux limites paraboliques dans un domaine non régulier.) (French. Abridged English version) Zbl 0783.35024
Summary: It is well known that the solution of a boundary value problem on a domain with a conical singularity admits a decomposition into a singular part and a regular one (see for instance the results of Kondrat’ev, Maz’ya-Plamenevskij, Grisvard and Dauge). Here we get analogous decomposition for parabolic problems on a cylinder with a polygonal basis. We extend on one hand the results of M. Moussaoui and B. K. Sadallah, P. Grisvard and A. Hammoudi concerning the heat equation and on the other hand those of V. S. Agranovich and M. I. Vishik and J.-L. Lions, where general parabolic problems are treated on smooth domains.
35K35 Initial-boundary value problems for higher-order parabolic equations
35C99 Representations of solutions to partial differential equations
35D10 Regularity of generalized solutions of PDE (MSC2000)