Maximal \(L_p\)-regularity of parabolic problems with boundary dynamics of relaxation type
The authors face interesting problems, such as dynamic boundary problems and linearized free boundary value problems in the context of the general theory of vector valued parabolic initial boundary value problems of relaxion type. They are able to get a very general \(L^p\) regularity theory. They use the tool of semigroup theory to get the maximal regularity for some model problems and then they are able to get the required result in the general case. All these results are obtained under the Lopatinskii-Shapiro conditions that the authors prove to be necessary conditions.
parabolic initial boundary value problems
scientific article; zbMATH DE number 5480705