Biharmonic Equations
Dirk Pauly, Alberto Valli
TL;DR
This paper develops and analyzes variational and operator methods for solving boundary value problems related to the biharmonic operator, focusing on Neumann and other boundary conditions.
Contribution
It introduces well-posed variational formulations and operator approaches for various boundary value problems involving the biharmonic operator.
Findings
Established well-posedness of variational formulations
Analyzed boundary value problems with Neumann and other conditions
Provided operator theoretical methods for biharmonic equations
Abstract
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined (maximal and minimal) boundary value problems.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Partial Differential Equations · Differential Equations and Boundary Problems · Holomorphic and Operator Theory