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

1990 ◽  
Vol 87 (1) ◽  
pp. 27-77 ◽  
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

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

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).

Linear second order elliptic equations with Venttsel boundary conditions

1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
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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