Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
Global Hölder estimates for equations of Monge-Ampère type.
Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that...
Global optimal regularity for the parabolic polyharmonic equations.
Global Regular Solutions for the Dynamic Antiplane Shear Problem in Nonlinear Viscoelasticity.
Global regularity for solutions of the minimal surface equation with continuous boundary values
Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity and with natural growth
In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for...
Global regularity for the 3D MHD system with damping
We study the Cauchy problem for the 3D MHD system with damping terms and (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.
Global Regularity of Solutions of Nonlinear Second Order Elliptic and Parabolic Differential Equations.
Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions.
Global Schauder estimates for a class of degenerate Kolmogorov equations
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
Global strong solutions of a 2-D new magnetohydrodynamic system
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 --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
Gradient estimates for the p(x)-Laplacian equation in
Under some assumptions on the function p(x), we obtain global gradient estimates for weak solutions of the p(x)-Laplacian type equation in .
Gradient estimates for weak solutions of -harmonic equations.
Gradient potential estimates
Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.
Gradient regularity via rearrangements for -Laplacian type elliptic boundary value problems
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.
Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains.