Remarques sur l'homogénéisation de certains problèmes quasi-linéaires
Remarques sur l’observabilité pour l’équation de Laplace
Nous quantifions la propriété de continuation unique pour le laplacien dans un domaine borné quand la condition aux bords est a priori inconnue. Nous établissons une estimation de dépen-dance de type logarithmique suivant la terminologie de John [5]. Les outils utilisés reposent sur les inégalités de Carleman et les techniques des travaux de Robbiano [8, 11]. Aussi, nous déterminons en application de l’inégalité d’observabilité obtenue un coût du contrôle approché pour un problème elliptique modèle....
Remarques sur l'observabilité pour l'équation de Laplace
We consider the Laplace equation in a smooth bounded domain. We prove logarithmic estimates, in the sense of John [5] of solutions on a part of the boundary or of the domain without known boundary conditions. These results are established by employing Carleman estimates and techniques that we borrow from the works of Robbiano [8,11]. Also, we establish an estimate on the cost of an approximate control for an elliptic model equation.
Removable sets for Hölder continuous -harmonic functions on metric measure spaces.
Removable singularities for bounded -harmonic functions and quasi(super)harmonic functions.
Removable singularities for Hölder continuous quasiregular mappings in the plane.
Removable singularities for the Yang-Mills-Higgs equations in two dimensions
Removable singularities for weak solutions of quasilinear elliptic systems.
Removable singularities of solutions to elliptic Monge-Ampère equations.
Removable Singularities of Some Strongly Nonlinear Elliptic Equations.
Removeable singular sets of fully nonlinear elliptic equations.
Renormalized entropy solutions for degenerate nonlinear evolution problems.
Renormalized solutions for nonlinear degenerate elliptic problems with L1 data.
Renormalized solutions of elliptic equations with general measure data
Represenation of a p-harmonic function near a critical point in the plane.
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of the L∞ norms of gradient fields. The...
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit...
Representation of Green's function for the Dirichlet problem of polyharmonic equations in a ball.
Reproduzierende Kerne, Fundamentalkerne und Resolventenkerne.
Řešení biharmonického problému pro nekonečný klín. I.