NONSYMMETRIC ELLIPTIC OPERATORS WITH WENTZELL BOUNDARY CONDITIONS IN GENERAL DOMAINS

被引：5

作者：

Favini, Angelo ^{[1
]}

Goldstein, Gisele Ruiz ^{[2
]}

Goldstein, Jerome A. ^{[2
]}

Obrecht, Enrico ^{[1
]}

Romanelli, Silvia ^{[3
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

[2] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[3] Univ Bari Aldo Moro, Dipartimento Matemat, I-70125 Bari, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 06期

关键词：

Nonsymmetric elliptic operators on general domains; Wentzell boundary conditions; analytic semigroups; perturbation of symmetric elliptic operators; continuous dependence; CONTINUOUS DEPENDENCE; SEMIGROUPS;

D O I：

10.3934/cpaa.2016045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study nonsymmetric second order elliptic operators with Wentzell boundary conditions in general domains with sufficiently smooth boundary. The ambient space is a space of L-p - type, 1 <= p <= infinity. We prove the existence of analytic quasicontractive (C-0)-semigroups generated by the closures of such operators, for any 1 < p < infinity. Moreover, we extend a previous result concerning the continuous dependence of these semigroups on the coefficients of the boundary condition. We also specify precisely the domains of the generators explicitly in the case of bounded domains and 1 < p < infinity, when all the ingredients of the problem, including the boundary of the domain, the coefficients, and the initial condition, are of class C-infinity.

引用

页码：2475 / 2487

页数：13

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