An existence theorem for the Dirichlet problem in the elastodynamics of incompressible materials

1988 ◽  
Vol 102 (2) ◽  
pp. 95-117 ◽  
Author(s):  
William J. Hrusa ◽  
Michael Renardy
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Incompressible Materials

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 On the Dirichlet problem of prescribed mean curvature equations without H-convexity condition

2000 ◽  
Vol 157 ◽  
pp. 177-209 ◽  
Author(s):  
Kazuya Hayasida ◽  
Masao Nakatani
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Existence Theorem ◽  
Mean Curvature ◽  
Weak Sense ◽  
Convexity Condition ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equations ◽  
Well Posed

The Dirichlet problem of prescribed mean curvature equations is well posed, if the boundery is H-convex. In this article we eliminate the H-convexity condition from a portion Γ of the boundary and prove the existence theorem, where the boundary condition is satisfied on Γ in the weak sense.

scholarly journals A Priori Bounds for a Class of Elliptic Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Differential Operators ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
A Priori Bounds ◽  
Uniqueness And Existence

We obtain some a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.

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