Free boundary value problems for abstract elliptic equations and applications

Abstract

Free bondary value problem for elliptic differential-operator equations with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued Holder spaces. 2010: 35xx, 47Fxx, 47Hxx, 35Pxx MSC

Fractional abstract Boussinesq equations and applications

“…In view of[39, Result 2.4] we obtain that A 1 is a sectorial operator in L p1 R d and by virtue of[4, § 3.14, 3.16] the operator A 1 is generator of bounded cosine function in L p1 R d . Moreover, in view of (4:1) by using the the Condition 4.1 we deduced that all assumptions of Theorem 2.1 are satis…ed, This implies the conclusion.…”