Abstract
In this paper, the separability properties of elliptic convolution operator equations are investigated. It is obtained that the corresponding convolution-elliptic operator is positive and also is a generator of an analytic semigroup. By using these results, the existence and uniqueness of maximal regular solution of the nonlinear convolution equation is obtained in spaces. In application, maximal regularity properties of anisotropic elliptic convolution equations are studied. MSC:34G10, 45J05, 45K05.
Highlights
Maximal regularity properties for differential operator equations, especially parabolic and elliptic-type, have been studied extensively, e.g., in [ – ] and the references therein (for comprehensive references, see [ ])
In recent years, maximal regularity properties for differential operator equations, especially parabolic and elliptic-type, have been studied extensively, e.g., in [ – ] and the references therein
In [, ], on theorems on the multiplicators of Fourier integrals obtained, which were used in studying isotropic as well as anisotropic spaces of differentiable functions of many variables
Summary
Maximal regularity properties for differential operator equations, especially parabolic and elliptic-type, have been studied extensively, e.g., in [ – ] and the references therein (for comprehensive references, see [ ]). In [ , ], on embedding theorems and maximal regular differential operator equations in Banach-valued function spaces have been studied. Let be a domain in Rn. C( ; E) and C(m)( ; E) will denote the spaces of E-valued bounded uniformly strongly continuous and m-times continuously differentiable functions on , respectively.
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