Separable Differential Operators with Parameters
In this paper, we study boundary value problems for parameter-dependent elliptic differential-operator equations with variable coefficients in smooth domains. Uniform regularity properties and Fredholmness of this problem are obtained in vector-valued Lp-spaces. We prove that the corresponding differential operator is positive and is a generator of an analytic semigroup. Then, via maximal regularity properties of the linear problem, the existence and uniqueness of the solution to the nonlinear elliptic problem is obtained. As an application, we establish maximal regularity properties of the Cauchy problem for abstract parabolic equations, Wentzell-Robin-type mixed problems for parabolic equations, and anisotropic elliptic equations with small parameters.
M. Bohner and V. B. Shakhmurov, "Separable Differential Operators with Parameters," Differential Equations and Dynamical Systems, Springer Verlag, Jan 2020.
The definitive version is available at https://doi.org/10.1007/s12591-020-00542-8
Mathematics and Statistics
Keywords and Phrases
Banach-valued function spaces; Boundary value problems; Differential-operator equations; Interpolation of Banach spaces; Operator-valued multipliers; Semigroup of operators; Wentzell-Robin condition
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2020