SYMMETRY RESULT FOR SOME OVERDETERMINED VALUE PROBLEMS

2008 ◽  
Vol 49 (4) ◽  
pp. 479-494 ◽  
Author(s):  
MOHAMMED BARKATOU ◽  
SAMIRA KHATMI
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Neumann Problem ◽  
Compatibility Condition ◽  
Mean Curvature ◽  
Boundary Value ◽  
The Maximum Principle ◽  
The Mean ◽  
The Neumann Problem ◽  
Symmetry Result

AbstractThe aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

scholarly journals About solvability of some boundary value problems for poisson equation in the ball

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 939-946
Author(s):  
Maira Koshanova ◽  
Batirkhan Turmetov ◽  
Kairat Usmanov
Keyword(s):  
Boundary Value Problems ◽  
Neumann Problem ◽  
Poisson Equation ◽  
Fractional Order ◽  
Periodic Boundary ◽  
Differential Operators ◽  
Boundary Value ◽  
Periodic Boundary Value Problems ◽  
Circular Domains ◽  
The Neumann Problem

In the paper we study properties of some integro - differential operators of fractional order. As an application of the properties of these operators for Poisson equation we examine questions on solvability of a fractional analogue of the Neumann problem and analogues of periodic boundary value problems for circular domains. The exact conditions for solvability of these problems are found.

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

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