Global Hölder estimates for equations of Monge-Ampère type.
Global inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation of second order
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 maximal estimates for solutions to the Schrödinger equation
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field
Global Regularity of Solutions of Nonlinear Second Order Elliptic and Parabolic Differential Equations.
Global regularity of the solutions to the capillarity problem
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 solution of optimal shape design problems.
Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds.
Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
Gluing approximate solutions of minimum type on the Nehari manifold.
Gradient bounds and Liouville theorems for quasilinear elliptic equations
Gradient estimates for a new class of degenerate elliptic and parabolic equations
Gradient estimates for a nonlinear equation on complete noncompact manifolds
Let be a complete noncompact Riemannian manifold. We consider gradient estimates on positive solutions to the following nonlinear equation in , where , are two real constants and , is a smooth real valued function on and . When is finite and the -Bakry-Emery Ricci tensor is bounded from below, we obtain a gradient estimate for positive solutions of the above equation. Moreover, under the assumption that -Bakry-Emery Ricci tensor is bounded from below and is bounded from above,...
Gradient estimates for inverse curvature flows in hyperbolic space
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface....
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 estimation of a -harmonic map.
Gradient flows with metric and differentiable structures, and applications to the Wasserstein space
In this paper we summarize some of the main results of a forthcoming book on this topic, where we examine in detail the theory of curves of maximal slope in a general metric setting, following some ideas introduced in [11, 5], and study in detail the case of the Wasserstein space of probability measures. In the first part we derive new general conditions ensuring convergence of the implicit time discretization scheme to a curve of maximal slope, the uniqueness, and the error estimates. In the second...