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