Hölder continuity of normalized solutions of the Schrödínger equation.
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...
Hölder continuous solutions to Monge–Ampère equations
Let be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on with right hand side, . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range of the complex Monge-Ampère operator acting on -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with -density belong to and proving that has the...
Hölder regularity for nonhomogeneous elliptic systems with nonlinearity greater than two
Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension is less than or equal to .
Hölder regularity for solutions to complex Monge-Ampère equations
We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is and the right hand side has a density in for some p > 1, and prove the Hölder continuity of the solution.
Hölder regularity of solutions to second-order elliptic equations in nonsmooth domains.
Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients
Hölder solutions for the amorphous silicon system and related problems.
Hölder-continuity of solutions for some Schrödinger equations
Holes and obstacles
Homeomorphisms and Fredholm theory for perturbations of nonlinear Fredholm maps of index zero with applications.
Homoclinic-type solutions for an almost periodic semilinear elliptic equation on
Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis
Homogénéisation du problème des courants de Foucault dans un transformateur
Homogénéisation et perturbations dans un problème lié à l'échauffement d'un câble électrique
Homogeneous Carnot groups related to sets of vector fields
In this paper, we are concerned with the following problem: given a set of smooth vector fields on , we ask whether there exists a homogeneous Carnot group such that is a sub-Laplacian on . We find necessary and sufficient conditions on the given vector fields in order to give a positive answer to the question. Moreover, we explicitly construct the group law i as above, providing direct proofs. Our main tool is a suitable version of the Campbell-Hausdorff formula. Finally, we exhibit several...
Homogeneous estimates for oscillatory integrals.
Homogenization in chemical reactive flows.
Homogenization in elastodynamics with force term depending on time.
Homogenization in polygonal domains
We consider the homogenization of elliptic systems with -periodic coefficients. Classical two-scale approximation yields an error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis substantially extends previous results obtained for polygonal domains with sides of rational slopes.