On solvability of a general elliptic boundary value problem in H\"older~--- Zygmund spaces with variable smoothness

V. D. Kryakvin ; G. P. Omarova

Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 50-62.

Résumé

Fredholm solvability of an elliptic boundary value problem, corresponding to the Green operator from the L. Boutet de Monvel algebra on a smooth manifold with compact boundary is studied in the paper. The Hölder — Zygmund spaces with variable smoothness are considered as function spaces. Sufficient conditions are given for the Fredholm property of the Green operator from the considered algebra in such spaces.

Détail

Keywords: Boutet de Monvel algebra, Fredholm property, Hölder-Zygmund spaces of variable smoothness, smooth manifold with compact boundary.

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