Global Hölder estimates for equations of Monge-Ampère type.
Global Instability and Essential Spectrum in Semilinear Evolution Equations.
Global solutions and quenching to a class of quasilinear parabolic equations.
Global subanalytic solutions of Hamilton–Jacobi type equations
Gradient bounds and Liouville theorems for quasilinear elliptic equations
Grandient Estimates for Degenerate Diffusion Equations. I.
Ground states of nonlinear Schrödinger equations with potentials
Hardy's uncertainty principle, convexity and Schrödinger evolutions
We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schrödinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy’s version of the uncertainty principle. We also obtain corresponding results for heat evolutions.
Harmonické funkce a věty o průměru
Harnachk Inequalities for Solutions of General Second Order Parabolic Equations and Estimates of Their Hölder Constants.
Hessian measures. II.
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...
Homogenization of monotone parabolic problems with several temporal scales
In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and...
How parabolic free boundaries approximate hyperbolic fronts.
Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian
In this paper we consider the modified wave equation associated with a class of radial Laplacians generalizing the radial part of the Laplace-Beltrami operator on hyperbolic spaces or Damek-Ricci spaces. We show that the Huygens’ principle and the equipartition of energy hold if the inverse of the Harish-Chandra -function is a polynomial and that these two properties hold asymptotically otherwise. Similar results were established previously by Branson, Olafsson and Schlichtkrull in the case of...
Hypoellipticity, fundamental solution and Liouville type theorem for matrix-valued differential operators in Carnot groups
Improved theory for a nonlinear degenerate parabolic equation
Inégalités différentielles fonctionnelles du type elliptique
Inégalités isopérimétriques et applications. Domaines nodaux des fonctions propres
Initial limits of temperatures on arbitrary open sets.