Removable singularities for the Yang-Mills-Higgs equations in two dimensions
Removable singularities for weak solutions of quasilinear elliptic systems.
Removable singularities in the boundary conditions
Removable singularities of -differential forms and quasiregular mappings.
Removable singularities of solutions of nonlinear singular partial differential equations
1. Introduction. The study of singularities has been one of the main subjects of research in partial differential equations. In the case of linear equations the singularities are now pretty well understood; but in the nonlinear case there seems to be still very few studies. In this paper I want to discuss the singularities of solutions of a class of nonlinear singular partial differential equations in the complex domain. The class is only a model, but it helps one understand that the situation in...
Removable singularities of solutions of the heat equation with special growth
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 entropy solutions of scalar conservation laws
Renormalized solution for nonlinear degenerate problems in the whole space
We consider the general degenerate parabolic equation :We suppose that the flux is continuous, is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for initial data and source term. We establish the uniqueness of this type of solution under a structure condition and an assumption on the modulus of continuity of . The novelty of this work is that , , , , are not Lipschitz...
Renormalized solutions for nonlinear degenerate elliptic problems with L1 data.
Renormalized solutions of a nonlinear parabolic equation with double degeneracy.
Renormalized solutions of elliptic equations with general measure data
Represenation of a p-harmonic function near a critical point in the plane.
Représentation des fonctions de BMO et solutions dé l'équation ...b.
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 equilibrium solutions to the table problem of growing sandpiles
In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main...