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 Lp-type, 1 ≤ p ≤ ∞. We prove the existence of analytic quasicontractive (C0)-semigroups generated by the closures of such operators, for any 1 ≤ p ≤ ∞. 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 ≤ ∞, when all the ingredients of the problem, including the boundary of the domain, the coefficients, and the initial condition, are of class C∞.
Nonsymmetric elliptic operators with Wentzell boundary conditions in general domains / Favini, Angelo; Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Obrecht, Enrico; Romanelli, Silvia. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 15:6(2016), pp. 2475-2487. [10.3934/cpaa.2016045]
Nonsymmetric elliptic operators with Wentzell boundary conditions in general domains
FAVINI, ANGELO;OBRECHT, ENRICO;
2016
Abstract
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 Lp-type, 1 ≤ p ≤ ∞. We prove the existence of analytic quasicontractive (C0)-semigroups generated by the closures of such operators, for any 1 ≤ p ≤ ∞. 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 ≤ ∞, when all the ingredients of the problem, including the boundary of the domain, the coefficients, and the initial condition, are of class C∞.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
