Related papers: Multi-anisotropic gevrey regularity of hypoellipti…

We give a microlocal version of the theorem of iterates in multi-anisotropic Gevrey classes for multi-anisotropic hypoelliptic differential operators

We obtain an explicit H\"older regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor uniformly elliptic.

We prove global H\"older regularity for the solutions to the time-harmonic anisotropic Maxwell's equations, under the assumptions of H\"older continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same…

We consider the maximal regularity of a specific Vlasov-Fokker-Planck equation $\mathcal{A}u=f$ in the Euclidean space. The operator $\mathcal{A}=\Delta_{y}u-y\cdot \nabla_x{u}$ is an example of the Ornstein-Uhlenbeck operators. We prove…

We study almost periodic pseudodifferential operators acting on almost periodic functions $G_{\rm ap}^s(\rr d)$ of Gevrey regularity index $s \geq 1$. We prove that almost periodic operators with symbols of H\"ormander type…

We give existence and regularity results for solutions of some nonlinear elliptic problems. The equations we deal with are modeled on a problem which involves in its principal part an anisotropic operator, a Hardy-type potential, and a…

We discuss some estimates of subelliptic type related with vector fields satisfying the H\"ormander condition. Our approach makes use of a class of approximate exponentials maps. Such kind of estimates arises naturally in the study of…

Motivated by recent results on the (possibly conditional) regularity for time-dependent hypoelliptic equations, we prove a parabolic version of the Poincar\'e inequality, and as a consequence, we deduce a version of the classical Moser…

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of…

The sharp Gevrey hypoellipticity is provided for the following generalization of the M\'etivier operator, "Non-hypoellipticit\'e analytique pour $D_{x}^{2}+\left( x^{2} + y^{2}\right)D_{y}^{2}$" by G. M\'etivier, \begin{align*}…

We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new…

We obtain Calder\'on-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows…

The overall goal of this dissertation is to investigate certain classical results from harmonic analysis, replacing the Euclidean setting, the abelian structure and the elliptic Laplace operator with a non-commutative environment and…

In this paper, we obtain an improved H\"older regularity for quasiregular gradient mappings which was studied by Baernstein and Kovalev.

For a linear nonvariational operator structured on smooth H\"ormander's vector fields, with H\"older continuous coefficients, we prove a regularity result in the spaces of H\"older functions. We deduce an analogous regularity result for…

We show that the multi--quasi-ellipticity is a necessary and sufficient condition for the property of elliptic iterates to be hold for multi-quasi-homogenous differential operators.

In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge-Amp\`ere equations in the plane, under the assumption that one principle entry of the Hessian is strictly positive and an appropriately finite…

We prove that $L^2$ weak solutions to hypoelliptic equations with bounded measurable coefficients are H\"older continuous. The proof relies on classical techniques developed by De Giorgi and Moser together with the averaging lemma and…

We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by Galerkin methods. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic…

In this paper we study a class of anisotropic equations with a lower order term whose coefficients lay in Marcinkiewicz spaces. We prove some regularity results for local solutions requiring any control on the norm of the coefficients.