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An isomorphism theorem for parabolic problems in Hörmander spaces and its applications. (English) Zbl 1361.35072

Summary: We investigate a general parabolic initial-boundary value problem with zero Cauchy data in some anisotropic Hörmander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate Hörmander spaces. As an application of this result, we establish a theorem on the local increase in regularity of solutions to the problem. We also obtain new sufficient conditions under which the generalized derivatives, of a given order, of the solutions should be continuous.

MSC:

35K35 Initial-boundary value problems for higher-order parabolic equations
46B70 Interpolation between normed linear spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35B65 Smoothness and regularity of solutions to PDEs
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