The Meyer’s estimate of solutions to Zaremba problem for second-order elliptic equations in divergent form

Yurij A. Alkhutov; Gregory A. Chechkin

doi:10.5802/crmeca.87

The Meyer’s estimate of solutions to Zaremba problem for second-order elliptic equations in divergent form

Comptes Rendus. Mécanique ◽

10.5802/crmeca.87 ◽

2021 ◽

Vol 349 (2) ◽

pp. 299-304

Author(s):

Yurij A. Alkhutov ◽

Gregory A. Chechkin

Keyword(s):

Elliptic Equations ◽

Second Order ◽

Divergent Form ◽

Second Order Elliptic Equations

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On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front

Georgian Mathematical Journal ◽

10.1515/gmj.2003.543 ◽

2003 ◽

Vol 10 (3) ◽

pp. 543-548

Author(s):

V. A. Kondrat'ev ◽

V. A. Nikishkin

Keyword(s):

Boundary Value Problem ◽

Elliptic Equations ◽

Dirichlet Boundary ◽

Boundary Value ◽

Second Order ◽

Dirichlet Boundary Value Problem ◽

Asymptotics Of Solutions ◽

Divergent Form ◽

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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Properties of a solution of the Dirichlet problem for second-order elliptic equations in a class of domains with nonsmooth boundary. I

Lithuanian Mathematical Journal ◽

10.1007/bf00966149 ◽

1987 ◽

Vol 26 (2) ◽

pp. 153-163

Author(s):

K. Pileckas ◽

K. Samaitis

Keyword(s):

Dirichlet Problem ◽

Elliptic Equations ◽

Second Order ◽

Nonsmooth Boundary ◽

Second Order Elliptic Equations

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Regularity of the generalized solutions of the first boundary-value problem for quasilinear degenerate second-order elliptic equations

Journal of Soviet Mathematics ◽

10.1007/bf01788913 ◽

1984 ◽

Vol 25 (1) ◽

pp. 815-832 ◽

Cited By ~ 1

Author(s):

A. V. Ivanov

Keyword(s):

Boundary Value Problem ◽

Elliptic Equations ◽

Boundary Value ◽

Second Order ◽

Generalized Solutions ◽

Second Order Elliptic Equations

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On Regularity and Existence of Viscosity Solutions of Nonlinear Second Order, Elliptic Equations

Partial Differential Equations and the Calculus of Variations ◽

10.1007/978-1-4684-9196-8_41 ◽

1989 ◽

pp. 939-957 ◽

Cited By ~ 6

Author(s):

Neil S. Trudinger

Keyword(s):

Viscosity Solutions ◽

Elliptic Equations ◽

Second Order ◽

Regularity And Existence ◽

Second Order Elliptic Equations

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The Dirichlet Problem for Two-Dimensional Quasi-Linear Second-Order Elliptic Equations

Linear Operators and Operator Equations ◽

10.1007/978-1-4757-0013-8_7 ◽

1971 ◽

pp. 115-125

Author(s):

N. M. Ivochkina

Keyword(s):

Dirichlet Problem ◽

Elliptic Equations ◽

Second Order ◽

Two Dimensional ◽

Second Order Elliptic Equations

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Three sphere inequality for second order elliptic equations with coefficients with jump discontinuity

Journal of Differential Equations ◽

10.1016/j.jde.2018.07.069 ◽

2019 ◽

Vol 266 (2-3) ◽

pp. 936-941 ◽

Cited By ~ 3

Author(s):

Michele Di Cristo ◽

Yong Ren

Keyword(s):

Elliptic Equations ◽

Second Order ◽

Jump Discontinuity ◽

Three Sphere ◽

Second Order Elliptic Equations

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The Behavior of Solutions to the Dirichlet Problem for Second Order Elliptic Equations with Variable Nonlinearity Exponent in a Neighborhood of a Conical Boundary Point

Journal of Mathematical Sciences ◽

10.1007/s10958-015-2570-7 ◽

2015 ◽

Vol 210 (4) ◽

pp. 341-370 ◽

Cited By ~ 3

Author(s):

Yu. Alkhutov ◽

M. V. Borsuk

Keyword(s):

Dirichlet Problem ◽

Boundary Point ◽

Elliptic Equations ◽

Second Order ◽

Second Order Elliptic Equations

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Sharp counterexamples in unique continuation for second order elliptic equations

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.2002.003 ◽

2002 ◽

Vol 2002 (542) ◽

Cited By ~ 3

Author(s):

Herbert Koch ◽

Daniel Tataru

Keyword(s):

Elliptic Equations ◽

Unique Continuation ◽

Second Order ◽

Second Order Elliptic Equations

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Maximum Principles for $P1$-Conforming Finite Element Approximations of Quasi-linear Second Order Elliptic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/110833737 ◽

2012 ◽

Vol 50 (2) ◽

pp. 626-642 ◽

Cited By ~ 18

Author(s):

Junping Wang ◽

Ran Zhang

Keyword(s):

Finite Element ◽

Elliptic Equations ◽

Second Order ◽

Maximum Principles ◽

Finite Element Approximations ◽

Conforming Finite Element ◽

Second Order Elliptic Equations

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High-order schemes of the finite elements method for second-order elliptic equations in three-dimensional domains. II

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(79)90098-3 ◽

1979 ◽

Vol 19 (5) ◽

pp. 54-61

Author(s):

V.G. Korneev

Keyword(s):

Finite Elements ◽

Elliptic Equations ◽

Three Dimensional ◽

Second Order ◽

High Order ◽

Finite Elements Method ◽

High Order Schemes ◽

Second Order Elliptic Equations

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