Solvability of Boundary Value Problems for Poisson's Equation in Unbounded Domains on Noncompact Riemannian Manifolds

被引：0

作者：

Mazepa, E. A. ^{[1
]}

机构：

[1] Volgograd State Univ, Volgograd 400064, Russia

来源：

DIFFERENTIAL EQUATIONS | 2020年 / 56卷 / 03期

关键词：

STATIONARY SCHRODINGER-EQUATION; DIRICHLET PROBLEM; INFINITY;

D O I：

10.1134/S0012266120030052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new approach is developed to posing boundary value problems on an arbitrary noncompact Riemannian manifold M. The approach is based on the introduction of classes of equivalent functions continuous on M. In particular, we establish dependence between the solvability of boundary value problems and exterior boundary value problems for some inhomogeneous linear elliptic equations on M.

引用

页码：324 / 329

页数：6

共 17 条

[1] NEGATIVELY CURVED MANIFOLDS, ELLIPTIC-OPERATORS, AND THE MARTIN BOUNDARY [J].

ANCONA, A .

ANNALS OF MATHEMATICS, 1987, 125 (03) :495-536

[2]

ANDERSON MT, 1983, J DIFFER GEOM, V18, P701

[3] DIFFERENTIAL EQUATIONS ON RIEMANNIAN MANIFOLDS AND THEIR GEOMETRIC APPLICATIONS [J].

CHENG, SY ;

YAU, ST .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1975, 28 (03) :333-354

[4]

Gilbarg D., 2001, ELLIPTIC PARTIAL DIF

[5] Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds [J].

Grigor'yan, A .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (02) :135-249

[6] On the solvability of boundary value problems for the stationary Schrodinger equation in unbounded domains on Riemannian manifolds [J].

Korol'kov, S. A. .

DIFFERENTIAL EQUATIONS, 2015, 51 (06) :738-744

[7] ON SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS FOR THE INHOMOGENEOUS ELLIPTIC EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS [J].

Losev, A. G. ;

Mazepa, E. A. .

PROBLEMY ANALIZA-ISSUES OF ANALYSIS, 2018, 7 :100-111

[8] Solvability of the Dirichlet Problem for the Poisson Equation on Some Noncompact Riemannian Manifolds [J].

Losev, A. G. .

DIFFERENTIAL EQUATIONS, 2017, 53 (12) :1595-1604

[9]

Losev A. G., 1999, Russ. Math, V43, P39

[10] On the hyperbolicity criterion for noncompact Riemannian manifolds of special type [J].

Losev, AG .

MATHEMATICAL NOTES, 1996, 59 (3-4) :400-404

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