IJPAM: Volume 88, No. 4 (2013)

ON THE EXISTENCE OF SOLUTIONS OF THE FIRST
BOUNDARY VALUE PROBLEM FOR ELLIPTIC
EQUATIONS ON UNBOUNDED DOMAINS

Armen L. Beklaryan
Department of Business Analytics
Higher School of Economics
National Research University
33, Kirpichnaya Str., Moscow, 105187, RUSSIA


Abstract. In this paper we consider the first boundary value problem for elliptic systems, defined on unbounded domains $\Omega \subset \mathbb{R}^n$, which solutions satisfy a condition of finiteness of the Dirichlet integral, also known as the energy integral

\begin{displaymath} \int\limits_{\Omega}\vert\nabla u\vert^2 dx<\infty. \end{displaymath}



Received: June 10, 2013

AMS Subject Classification: 35J25

Key Words and Phrases: elliptic equation, boundary value problem, Hardy inequality, capacity

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DOI: 10.12732/ijpam.v88i4.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 4