Boundary value problems with rough boundary data

被引:2
作者
Denk, Robert [1 ]
Ploss, David [1 ]
Rau, Sophia [1 ]
Seiler, Jorg [2 ]
机构
[1] Univ Konstanz, Fachbereich Math & Stat, Constance, Germany
[2] Univ Torino, Dipartimento Matemat, V Carlo Alberto 10, I-10123 Turin, Italy
关键词
Boundary value problem; Anisotropic Sobolev space; Generalized trace; Dynamic boundary condition; Holomorphic semigroup; REGULARITY; BEHAVIOR; SPACES;
D O I
10.1016/j.jde.2023.04.001
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 Lp(Rn+) x Lp(Rn-1). (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码:85 / 131
页数:47
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