Spectral bounds for the operator pencil of an elliptic system in an angle
Authors
- Tsopanopoulos, Michael
2020 Mathematics Subject Classification
- 35B30 35J47 35B65 47A10 47A12 47B44
Keywords
- Operator pencil, mixed boundary conditions, elliptic systems, higher regularity, numerical range, accretive operators
DOI
Abstract
The model problem of a plane angle for a second-order elliptic system with Dirichlet, mixed, and Neumann boundary conditions is analyzed. The existence of solutions is, for each boundary condition, reduced to solving a matrix equation. Leveraging these matrix equations and focusing on Dirichlet and mixed boundary conditions, optimal bounds on these solutions are derived, employing tools from numerical range analysis and accretive operator theory. The developed framework is novel and recovers known bounds for Dirichlet boundary conditions. The results for mixed boundary conditions are new and represent the central contribution of this work. Immediate applications of these findings are new regularity results in linear elasticity.
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