Regularity of the solution of the Cauchy problem for a higher-order parabolic equation
This paper is concerned with the regularity of solutions to some Cauchy problems of parabolic type of order \(2m\). The author obtains the solvability of such problems in the class of weighted Hölder space of order \(2m\) by combining the method of potentials and the method of continuation with respect to a parameter. The only assumption required in the paper is that the right-hand side and lower order coefficients of the equation satisfy a certain growth condition when approaching the plane that is the support of the initial data while the higher order are not required to satisfy the Dini condition near the support plane.
scientific article; zbMATH DE number 5824105