AN ISOMORPHISM THEOREM FOR PARABOLIC PROBLEMS IN HORMANDER SPACES AND ITS APPLICATIONS

作者：Los Valerii; Mikhailets Vladimir A; Murach Aleksandr A^*

来源：Communications on Pure and Applied Analysis, 2017, 16(1): 69-97.

DOI：10.3934/cpaa.2017003

• Parabolic initial-boundary value problem
• Hormander space
• slowly varying function
• isomorphism property
• interpolation with a function parameter

We investigate a general parabolic initial-boundary value problem with zero Cauchy data in some anisotropic Hormander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate Hormander 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.

• 出版日期2017-1