Well-posedness of the second-order linear singular Dirichlet problem

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Alexander Lomtatidze ◽  
Zdeněk Opluštil
Keyword(s):  
Dirichlet Problem ◽  
Second Order ◽  
Well Posedness ◽  
Order Linear ◽  
Singular Dirichlet Problem

AbstractConditions guaranteeing well-posedness of the problem

scholarly journals The Dirichlet Problem for elliptic equations in unbounded domains of the plane

2008 ◽  
Vol 6 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Paola Cavaliere ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Elliptic Equations ◽  
Unbounded Domains ◽  
Suitable Condition ◽  
Second Order ◽  
Order Linear ◽  
Uniqueness And Existence

In this paper we prove a uniqueness and existence theorem for the Dirichlet problem inW2,pfor second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of classVMOand satisfy a suitable condition at infinity.

scholarly journals The second order estimate for the solution to a singular elliptic boundary value problem

2012 ◽  
Vol 6 (2) ◽  
pp. 194-213 ◽  
Author(s):  
Ling Mi ◽  
Liu Bin
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Smooth Boundary ◽  
Elliptic Boundary ◽  
Second Order ◽  
Variation Theory ◽  
Order Estimate ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Singular Dirichlet Problem

We study the second order estimate for the unique solution near the boundary to the singular Dirichlet problem -?u = b(x)g(u); u > 0; x ? ?, u|?? = 0, where ? is a bounded domain with smooth boundary in RN, g ? C1((0,?),(0?)), g is decreasing on (0,?) with lim s?0+ g(s) = 1 and g is normalized regularly varying at zero with index ? (? > 1), b ? C?(??) (0 < ? < 1), is positive in ?, may be vanishing on the boundary. Our analysis is based on Karamata regular variation theory.

SOLUSI LEMAH MASALAH DIRICHLET PERSAMAAN DIFERENSIAL PARSIAL LINEAR ELIPTIK ORDER DUA

2018 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Sekar Nugraheni ◽  
Christiana Rini Indrati
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Elliptic Partial Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Order Linear ◽  
Definition Of

The weak solution is one of solutions of the partial differential equations, that is generated from derivative of the distribution. In particular, the definition of a weak solution of the Dirichlet problem for second order linear elliptic partial differential equations is constructed by the definition and the characteristics of Sobolev spaces on Lipschitz domain in R^n. By using the Lax Milgram Theorem, Alternative Fredholm Theorem and Maximum Principle Theorem, we derived the sufficient conditions to ensure the uniqueness of the weak solution of Dirichlet problem for second order linear elliptic partial differential equations. Furthermore, we discussed the eigenvalue of Dirichlet problem for second order linear elliptic partial differential equations with  respect to the weak solution.

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