scholarly journals The Boundary Value Problems for Non-Linear Elliptic Equations and the Maximum Principle for Euler-Lagrange Equations

1989 ◽  
pp. 181-210
Author(s):  
Ilya J. Bakelman
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Lagrange Equations ◽  
The Maximum Principle ◽  
Non Linear

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 Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

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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