The blow-up rate for a semilinear parabolic equation with a nonlinear boundary condition.
The Cauchy problem for a nonlinear Wheeler-DeWitt equation
The Dirichlet problem for elliptic equations with drift terms.
We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.
The existence of solutions for elliptic systems with nonuniform growth
We study the Dirichlet problems for elliptic partial differential systems with nonuniform growth. By means of the Musielak-Orlicz space theory, we obtain the existence of weak solutions, which generalizes the result of Acerbi and Fusco [1].
The Generalized Ahlfors-Heins Theorem in Certain d-Dimensional Cones.
The growth of entire solutions of differential equations of finite and infinite order
For certain Fréchet spaces of entire functions of several variables satisfying some specified growth conditions, we define a constant coefficient differential operator as the transpose of a convolution operation in the dual space of continuous linear functionals and show that for in one of these spaces, their always exists a solution of the differential equation in the same space.
The index of isolated critical points and solutions of elliptic equations in the plane
The microstructure of Lipschitz solutions for a one-dimensional logarithmic diffusion equation
We consider the initial-boundary-value problem for the one-dimensional fast diffusion equation on . For monotone initial data the existence of classical solutions is known. The case of non-monotone initial data is delicate since the equation is singular at . We ‘explicitly’ construct infinitely many weak Lipschitz solutions to non-monotone initial data following an approach to the Perona-Malik equation. For this construction we rephrase the problem as a differential inclusion which enables us...
The nonlinear membrane model : a Young measure and varifold formulation
We establish two new formulations of the membrane problem by working in the space of -Young measures and -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences...
The nonlinear membrane model: a Young measure and varifold formulation
We establish two new formulations of the membrane problem by working in the space of -Young measures and -varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...
The oscillatory behavior of second order nonlinear elliptic equations.
The sharp Poincaré inequality for free vector fields: an endpoint result.
The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms
The Tartar equation for homogenization of a model of the dynamics of fine-dispersion mixtures.
The Total Variation of Solutions of Parabolic Differential Equations and a Maximum Principle in Unbounded Domains.
The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
The zero set of a solution of a parabolic equation.
Thin vortex tubes in the stationary Euler equation
In this paper we outline some recent results concerning the existence of steady solutions to the Euler equation in with a prescribed set of (possibly knotted and linked) thin vortex tubes.
Time Decay for Nonlinear Wave Equations in Two Space Dimensions.
Time Decay for Some Schrödinger Equations.