Abstract
In this paper we give some results on abstract second order differential elliptic equations of mixed type. The study is performed in Holder continuous Banach spaces. Our main purpose is the study of necessary and sufficient conditions on the data for obtaining existence, uniqueness and maximal regularity properties of the strict solution. The techniques used are based on analytic semigroups theory.
Highlights
U0 is a given element in X and A is a closed linear operator of domain D(A) not necessarily dense in X
In this paper we give some results on abstract second order differential elliptic equations of mixed type
The study is performed in Holder continuous Banach spaces
Summary
U0 is a given element in X and A is a closed linear operator of domain D(A) not necessarily dense in X. Our main purpose is the study of necessary and sufficient conditions on the data for obtaining existence, uniqueness and maximal regularity properties of the strict solution. Let X be a complex Banach space and consider the second order abstract differential problem u (x) + Au(x) = f (x), x ∈ [0, 1]
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