ON THE QUESTION OF THE UNIQUENESS OF THE SOLUTION OF THE SECOND BOUNDARY VALUE PROBLEM FOR SECOND ORDER ELLIPTIC EQUATIONS

Abstract Two terms of asymptotics near crack are obtained for solutions of the Dirichlet boundary value problem for second-order elliptic equations in divergent form. The front of a crack is from 𝐶1+𝑠 and the coefficients of the equations belong to 𝐶𝑠 (0.5 < 𝑠 < 1).

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The mixed boundary-value problem for second order elliptic equations with degenerate curve on the sides of an angle

Mathematische Nachrichten ◽

10.1002/mana.200310440 ◽

2006 ◽

Vol 279 (13-14) ◽

pp. 1602-1613 ◽

Cited By ~ 8

Author(s):

Guochun Wen

Keyword(s):

Boundary Value Problem ◽

Elliptic Equations ◽

Mixed Boundary ◽

Boundary Value ◽

Second Order ◽

Mixed Boundary Value Problem ◽

Degenerate Curve ◽

Second Order Elliptic Equations

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The probabilistic solution of the third boundary value problem for second order elliptic equations

Probability Theory and Related Fields ◽

10.1007/bf01217746 ◽

1990 ◽

Vol 87 (1) ◽

pp. 27-77 ◽

Cited By ~ 20

Author(s):

Vassilis G. Papanicolaou

Keyword(s):

Boundary Value Problem ◽

Elliptic Equations ◽

Boundary Value ◽

Second Order ◽

The Third ◽

Probabilistic Solution ◽

Second Order Elliptic Equations ◽

Third Boundary Value Problem

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Nonnegative solutions of the first boundary-value problem for second-order elliptic equations with a boundary function equal to infinity at a boundary point

Journal of Soviet Mathematics ◽

10.1007/bf01086110 ◽

1986 ◽

Vol 33 (4) ◽

pp. 1067-1082

Author(s):

D. A. Krupskaya

Keyword(s):

Boundary Value Problem ◽

Boundary Point ◽

Elliptic Equations ◽

Boundary Value ◽

Boundary Function ◽

Second Order ◽

Nonnegative Solutions ◽

Second Order Elliptic Equations

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On the uniqueness of the solution of a two-point second boundary value problem for a second-order simple differential equation solved by the bernoulli equation

ACADEMICIA An International Multidisciplinary Research Journal ◽

10.5958/2249-7137.2021.02026.7 ◽

2021 ◽

Vol 11 (9) ◽

pp. 969-973

Author(s):

M.Y. Qosimova ◽

N.X. Yusupova ◽

S.T. Qosimova

Keyword(s):

Differential Equation ◽

Boundary Value Problem ◽

Boundary Value ◽

Second Order ◽

Bernoulli Equation ◽

Uniqueness Of The Solution

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ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

Mathematical Modelling and Analysis ◽

10.3846/13926292.2001.9637154 ◽

2001 ◽

Vol 6 (1) ◽

pp. 147-155 ◽

Cited By ~ 1

Author(s):

S. Rutkauskas

Keyword(s):

Boundary Value Problem ◽

Existence And Uniqueness ◽

Boundary Value ◽

Elliptic Systems ◽

Second Order ◽

Type Problem ◽

Dirichlet Type ◽

Holder Class ◽

Uniqueness Of The Solution ◽

Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

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Approximate method for solving discontinuous boundary value problem of non-linear elliptic equations of second order

Complex Variables and Elliptic Equations ◽

10.1080/17476933.2013.819570 ◽

2013 ◽

Vol 59 (8) ◽

pp. 1143-1155

Author(s):

Guochun Wen

Keyword(s):

Boundary Value Problem ◽

Approximate Method ◽

Elliptic Equations ◽

Boundary Value ◽

Second Order ◽

Discontinuous Boundary ◽

Non Linear

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Linear second order elliptic equations with Venttsel boundary conditions

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500029048 ◽

1991 ◽

Vol 118 (3-4) ◽

pp. 193-207 ◽

Cited By ~ 28

Author(s):

Yousong Luo ◽

Neil S. Trudinger

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Elliptic Equations ◽

Existence Result ◽

Boundary Value ◽

Second Order ◽

Classical Solutions ◽

Schauder Estimate ◽

Second Order Elliptic Equations

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

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