In this paper we consider elliptic problems with an operator depending only on the deformation tensor. We consider the class of operators derived from a potential and with (p,delta)-structure, for 1<=2 and for all delta>=0. We apply the so called A-approximation method to approximate the operator by another one with linear growth. This allows us to prove the ``natural'' second order regularity (up to the boundary) in the case of homogeneous Dirichlet boundary conditions. Results are not completely new, but the method we apply was not used before in this setting.
Natural second order regularity for systems in the case 1<=2 using the A-approximation
Luigi C. Berselli;
2022-01-01
Abstract
In this paper we consider elliptic problems with an operator depending only on the deformation tensor. We consider the class of operators derived from a potential and with (p,delta)-structure, for 1<=2 and for all delta>=0. We apply the so called A-approximation method to approximate the operator by another one with linear growth. This allows us to prove the ``natural'' second order regularity (up to the boundary) in the case of homogeneous Dirichlet boundary conditions. Results are not completely new, but the method we apply was not used before in this setting.File in questo prodotto:
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