|Title||Fourier multipliers in the spaces with partial Hölder property and their application to the Schauder estimates|
|Publication Type||Journal Article|
|Year of Publication||2014|
|Abbreviated Key Title||Dopov. Nac. akad. nauk Ukr.|
We give relatively simple sufficient conditions for a Fourier multiplier in order that it maps functions with the Hölder property in a part of the variables into functions with the Hölder property in all variables. With the use of these sufficient conditions, we prove the solvability in Hölder classes of the initial-boundary-value problems for a linearized Cahn–Hilliard equation with dynamic boundary conditions of two types. For the solutions of these problems, the Schauder estimates are obtained.
|Keywords||Fourier multipliers, Hölder property, Schauder estimates, spaces|
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