Eigencurves for linear elliptic equations

Rivas, Mauricio A.¹  ; Robinson, Stephen B.¹

¹

ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 45.

Résumé

This paper provides results for variational eigencurves associated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a, b, m) of continuous symmetric bilinear forms on a real separable Hilbert space V . Geometric characterizations of eigencurves associated with (a, b, m) are obtained and are based on their variational characterizations described here. Continuity, differentiability, as well as asymptotic, results for these eigencurves are proved. Finally, two-parameter Robin–Steklov eigenproblems are treated to illustrate the theory.

Détail

Reçu le : 2017-05-27
Accepté le : 2018-06-18
DOI : 10.1051/cocv/2018039

Classification : 35J20, 35P15, 58J20
Keywords: Two-parameter eigenproblems, variational eigencurves, Robin–Steklov eigenproblems

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