Global regularity for nonlinear systems with symmetric gradients. (English) Zbl 1534.35146
Summary: We study global regularity of nonlinear systems of partial differential equations depending on the symmetric part of the gradient with Dirichlet boundary conditions. These systems arise from variational problems in plasticity with power growth. We cover the full range of exponents \(p\in(1, \infty)\). As a novelty the degenerate case for \(p > 2\) is included. We present a unified approach for all exponents by showing the regularity for general systems of Orlicz growth.
MSC:
| 35J57 | Boundary value problems for second-order elliptic systems |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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