116 research outputs found
Nonlinear oblique boundary value problems for nonlinear elliptic equations
No full textWe consider the nonlinear oblique derivative boundary value problem for quasilinear and fully nonlinear uniformly elliptic partial differential equations of second order. The elliptic operators satisfy natural structure conditions as introduced by Trudinger in the study of the Dirichlet problem while for the boundary operators we formulate general structure conditions which embrace previously considered special cases such as the capillarity condition. The resultant existence theorems include previous work such as that of Lieberman on quasilinear equations and Lions and Trudinger on Neumann boundary conditions.</p
Schauder estimates for fully nonlinear elliptic difference operators
No full textIn this paper, we are concerned with discrete Schauder estimates for solutions of fully nonlinear elliptic difference equations. Our estimates are discrete versions of second derivative Holder estimates of Evans, Krylov and Safonov for fully nonlinear elliptic partial differential equations. They extend previous results of Holt by for the special case of functions of pure second-order differences on cubic meshes. As with Holtby's work, the fundamental ingredients are the pointwise estimates of Kuo-Trudinger for linear difference schemes on general meshes
Elliptic partial differential equations of second order (book review)
No full textThis book is the reprint of the 1998 edition of Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S. Trudinger that originally appeared in 1977
Recommended from our members
Partielle Differentialgleichungen
No full textThe workshop dealt with partial differential equations in geometry and technical applications. The main topics were the combination of nonlinear partial differential equations and geometric problems, regularity of free boundaries, conformal invariance and the Willmore functional
On the convexity theory of generating functions
No full textIn this paper, we extend our convexity theory for cost functions in
optimal transportation to more general generating functions, which were
originally introduced by the second author to extend the framework of optimal
transportation to embrace near field geometric optics. In particular we provide
an alternative geometric treatment to the previous analytic approach using
differential inequalities, which also gives a different derivation of the
invariance of the fundamental regularity conditions under duality. We also
extend our local theory to cover the strict version of these conditions for
cost and generating functions.Comment: Some typos corrected in previous version and comments adde
Optimal transport with discrete long-range mean-field interactions
No full text2020 The Author(s). The Author(s). We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma-Trudinger-Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151-183.]
Some results on Hessian measures for non-commuting vector fields(Viscosity Solution Theory of Differential Equations and its Developments)
No full text
- …
