The Nikol’Skii Type Regularity of Solutions to Nonlinear Problems in Domains with Hölder Boundary

We study the regularity of solutions to problems of minimization of integral functionals, the Dirichlet and Neumann problems for elliptic operators of order 2m in domains with Hölder boundary on a compact Riemannian manifold. We establish interactions between the smoothness of the right-hand side, the regularity of the boundary, and the smoothness of solutions to the problems under consideration. Bibliography: 10 titles. © 2016, Springer Science+Business Media New York.