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Korn’s inequalities for generalized external cusps
(Wiley, 2016-11)
In this paper we consider a general class of external cusps defined by linking appropriate collections of John domains. For that class, weighted Korn inequalities are proved by means of rather elementary arguments.
The Korn inequality for Jones domains
(Texas State University. Department of Mathematics, 2004-12)
In this paper we prove the Korn inequality, and its generalization to Lp, 1 < p < ∞, for bounded domains Ω ⊂ Rn, n ≥ 2, satisfying an ( , δ) condition.
Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
(American Mathematical Society, 2013-01)
The Korn inequality and related results on solutions of the divergence in Sobolev spaces have been widely studied since the pioneering works by Korn and Friedrichs. In particular, it is known that this inequality is valid ...
Solutions of the divergence and Korn inequalities on domains with an external cusp
(Suomalainen Tiedeakatemia, 2010-08)
This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are ...
Minimization of energy functionals in elasticity
(2013)
Uno de los principales problemas en la teoría matemática de cuerpos elásticos es probar la existencia de estados de equilibrio de un cuerpo elástico sometido a fuerzas externas, sin embargo debido a la gran cantidad de ...
On weak solvability of boundary value problems for elliptic systems
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 2013)
This paper concerns with existence and uniqueness of a weak solution for elliptic systems of partial differential equations with mixed boundary conditions. The proof is based on establishing the coerciveness of bilinear ...
An elementary proof of the continuity from L20(Ω) to H10(Ω)n of Bogovskii’s right inverse of the divergence
(Unión Matemática Argentina, 2012-03)
The existence of right inverses of the divergence as an operator from H1 0 (Ω)n to L 2 0(Ω) is a problem that has been widely studied because of its importance in the analysis of the classic equations of fluid dynamics. ...