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Global Schauder estimates for a class of degenerate Kolmogorov equations

Enrico Priola (2009)

Studia Mathematica

We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...

Global Strichartz estimates for variable coefficient second order hyperbolic operators

Daniel Tataru (1999/2000)

Séminaire Équations aux dérivées partielles

Global strong solutions of a 2-D new magnetohydrodynamic system

Ruikuan Liu, Jiayan Yang (2020)

Applications of Mathematics

The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on $L^{p}$ - $L^{q}$ -estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.

Gradient estimates for a new class of degenerate elliptic and parabolic equations

Gary M. Lieberman (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Gradient estimates for the p(x)-Laplacian equation in $ℝ^{N}$

Chao Zhang, Shulin Zhou, Bin Ge (2015)

Annales Polonici Mathematici

Under some assumptions on the function p(x), we obtain global gradient estimates for weak solutions of the p(x)-Laplacian type equation in $ℝ^{N}$ .

Gradient estimates for weak solutions of $𝒜$ -harmonic equations.

Yao, Fengping (2010)

Journal of Inequalities and Applications [electronic only]

Gradient potential estimates

Giuseppe Mingione (2011)

Journal of the European Mathematical Society

Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.

Gradient regularity via rearrangements for $p$ -Laplacian type elliptic boundary value problems

Andrea Cianchi, Vladimir G. Maz'ya (2014)

Journal of the European Mathematical Society

A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.

Grandient Estimates for Degenerate Diffusion Equations. I.

Nicholas D. Alikakos, Ruben Rostamian (1982)

Mathematische Annalen

Displaying 21 – 29 of 29

Currently displaying 21 – 29 of 29