On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces-Reference-Cited by-同舟云学术

On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces

Published:2024-06-21 Issue: Volume: Page:
ISSN:0170-4214
Container-title:Mathematical Methods in the Applied Sciences
language:en
Short-container-title:Math Methods in App Sciences

Author:

Bilalov Bilal T.¹²³^ORCID,Sadigova Sabina R.¹⁴,Sezer Yonca²,Nasibova Natavan P.⁵

Affiliation:

1. Department of “Non‐harmonic Analysis”, Institute of Mathematics and Mechanics The Ministry of Science and Education Baku Azerbaijan

2. Department of Mathematics Yildiz Technical University Istanbul Turkey

3. Department of Functional Analysis and Applications Azerbaijan University of Architecture and Construction Baku Azerbaijan

4. Department of Mathematics Khazar University Baku Azerbaijan

5. Department of General and Applied Mathematics Azerbaijan State Oil and Industry University Baku Azerbaijan

Abstract

Let be a bounded domain with sufficiently smooth boundary and be a symmetric space defined on the measure space . We consider a Dirichlet problem for ‐th order polyharmonic equation, and we establish its solvability (in strong sense) in Sobolev space generated by the norm of . Such spaces include classical Sobolev spaces, Orlicz–Sobolev spaces, grand Sobolev spaces, and Marcinkiewicz–Sobolev spaces. The obtained results are new for these special cases, too.

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.10279

Reference39 articles.

1. On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball

2. Regularity in Orlicz spaces for the Poisson equation

3. Regularity theory in Orlicz spaces for the parabolic polyharmonic equations;Yao F.;Arch. Math.,2008

4. Weighted a priori estimates for the Poisson equation;Duran R. G.;Indiana Univ. Math. J.,2008