Boundary value problems with rough boundary data

Autor:	Robert Denk, David Ploß, Sophia Rau, Jörg Seiler
Rok vydání:	2023
Předmět:	Boundary value problem Anisotropic Sobolev space Generalized trace Dynamic boundary condition Holomorphic semigroup Mathematics - Analysis of PDEs Applied Mathematics FOS: Mathematics 35J40 (primary) 46E35 47D06 35K35 (secondary) Analysis Analysis of PDEs (math.AP)
Zdroj:	Journal of Differential Equations. 366:85-131
ISSN:	0022-0396
DOI:	10.1016/j.jde.2023.04.001
Popis:	We consider linear boundary value problems for higher-order parameter-elliptic equations, where the boundary data do not belong to the classical trace spaces. We employ a class of Sobolev spaces of mixed smoothness that admits a generalized boundary trace with values in Besov spaces of negative order. We prove unique solvability for rough boundary data in the half-space and in sufficiently smooth domains. As an application, we show that the operator related to the linearized Cahn--Hilliard equation with dynamic boundary conditions generates a holomorphic semigroup in $L^p(\mathbb R^n_+)\times L^p(\mathbb R^{n-1})$. 41 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::975832ae7409401a92b048d9eef18bab https://doi.org/10.1016/j.jde.2023.04.001 Zobrazit plný text záznamu Full Text from ScienceDirect