On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces

• Main Author: Hovik Matevossian
• Format: Article
• Language: English
• Published: MDPI AG 2019-02-01
• Series: Mathematical and Computational Applications
• Subjects: biharmonic operator; mixed Dirichlet–Steklov-type problem; Steklov-type problem; Dirichlet integral; weighted spaces
• Online Access: https://www.mdpi.com/2297-8747/24/1/25

We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet&#8315;Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mi>a</mi></msup></semantics></math></inline-formula>. Depending on the value of the parameter <i>a</i>, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions.