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Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain $Ω \subset ℝ^{d}$ with a continuous piecewise smooth obstacle. We formulate a fully discrete method by using piecewise linear finite elements in space and the backward Euler method in time. We define an a posteriori error estimator and show that it gives an upper bound for the error in L2(0,T;H1(Ω)). The error estimator is localized in the sense that the size of the elliptic residual...

A principle of linearization in theory of stability of solutions of variational inequalities

Jiří Neustupa (1995)

Mathematica Bohemica

It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.

A remark on the local Lipschitz continuity of vector hysteresis operators

Pavel Krejčí (2001)

Applications of Mathematics

It is known that the vector stop operator with a convex closed characteristic $Z$ of class $C^{1}$ is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping $n$ is Lipschitz continuous on the boundary $\partial Z$ of $Z$ . We prove that in the regular case, this condition is also necessary.

A time periodic solution of the Navier-Stokes equations with mixed boundary conditions

Kučera, Petr (1998)

Proceedings of Equadiff 9

An abstract differential inequality and eigenvalues of variational inequalities

Jan Neumann (1987)

Commentationes Mathematicae Universitatis Carolinae

An optimal partial regularity result for minimizers of an intrinsically defined second-order functional

Christoph Scheven (2009)

Annales de l'I.H.P. Analyse non linéaire

Bifurcation points of variational inequalities

Milan Kučera (1982)

Czechoslovak Mathematical Journal

Bifurcation problems for nonlinear elliptic variational inequalities

Marco Degiovanni (1989)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Blow-up of solutions to a periodic nonlinear dispersive rod equation.

Jin, Liangbing, Liu, Yongming (2010)

Documenta Mathematica

Constantes de Sobolev des arbres

Marc Bourdon (2007)

Bulletin de la Société Mathématique de France

Étant donnés $p \in [1, + \infty [$ et un arbre $T$ dont chaque sommet est de valence au moins $3$ , on étudie la constante de Sobolev d’exposant $p$ de $T$ , c’est-à-dire la plus petite constante $σ_{p}$ telle que pour tout $u \in ℓ_{p} (T^{0})$ on ait ${∥ u ∥}_{p}^{p} \leq σ_{p} {∥ d u ∥}_{p}^{p}$ . Notre motivation vient de la recherche de graphes finis avec des petites constantes de Poincaré d’exposant $p$ , en vue d’obtenir des exemples de groupes qui ont la propriété de point fixe sur les espaces $L^{p}$ .

Contact problems with bounded friction. Semicoercive case

Jiří Jarušek (1984)

Czechoslovak Mathematical Journal

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