Some regularity properties of solutions of Monge Ampère equation

From MaRDI portal
Publication:4005704

DOI10.1002/cpa.3160440809zbMath0761.35028OpenAlexW2038392026MaRDI QIDQ4005704

Luis A. Caffarelli

Publication date: 27 September 1992

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160440809



Related Items

Global \(W^{2,p}\) regularity on the linearized Monge-Ampère equation with \(\text{VMO}\) Type coefficients, On a non-homogeneous version of a problem of Firey, The Orlicz Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity, Global \(C^{1,\alpha}\) regularity for Monge-Ampère equation and convex envelope, Convexity of the support of the displacement interpolation: counterexamples, Properties of the solutions to the Monge-Ampère equation, On the continuity of center-outward distribution and quantile functions, Fast $L^2$ Optimal Mass Transport via Reduced Basis Methods for the Monge--Ampère Equation, The Monge problem with vanishing gradient penalization: vortices and asymptotic profile, Stability results on the smoothness of optimal transport maps with general costs, Regularity of optimal transport maps on multiple products of spheres, Isoperimetric-type inequalities on constant curvature manifolds, Regularity of weak solutions to the Monge–Ampère equation, Hölder regularity of the 2D dual semigeostrophic equations via analysis of linearized Monge-Ampère equations, Entire invariant solutions to Monge-Ampère equations, On the Preservation of Eccentricities of Monge–Ampère Sections, $L^\infty $ estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems, A Nonlinear Mean Value Property for Monge-Amp\`ere, A Minkowski problem for electrostatic capacity, The Monge–Ampère equation and its link to optimal transportation, A global existence result for the semigeostrophic equations in three dimensional convex domains, Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications, Regularity of optimal transport between planar convex domains, The discrete logarithmic Minkowski problem for \(q\)-capacity, Monge-Ampère Equation with Bounded Periodic Data, Free boundary regularity in the optimal partial transport problem, \(W^{2,1+\varepsilon}\) estimates for the Monge-Ampère equation, The Hadamard variational formula and the Minkowski problem for \(p\)-capacity, Hölder continuity and injectivity of optimal maps, Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties, Strict convexity and \(C^{1,\alpha}\) regularity of potential functions in optimal transportation under condition A3w, A priori estimates and existence of solutions to the prescribed centroaffine curvature problem, On the regularity of solutions of optimal transportation problems, A Liouville theorem for the Neumann problem of Monge-Ampère equations, A generalization of Caffarelli's contraction theorem via (reverse) heat flow, Regularity of optimal transport maps and partial differential inclusions, A note on the regularity of optimal-transport-based center-outward distribution and quantile functions, \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation, Boundary regularity for solutions to the linearized Monge-Ampère equations, The functional Orlicz Brunn-Minkowski inequality for \(q\)-capacity, Lipschitz estimates on the JKO scheme for the Fokker-Planck equation on bounded convex domains, The \(L_p\) Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity, Gradient rearrangement for diffeomorphisms of a compact manifold., Interior estimates for Monge-Ampère equation in terms of modulus of continuity, Swirling fluid flow in flexible, expandable elastic tubes: variational approach, reductions and integrability, A \(L_p\) Brunn-Minkowski theory for logarithmic capacity, Real analysis related to the Monge-Ampère equation, On the free boundary associated with the stationary Monge-Ampère operator on the set of non strictly convex functions, Log-concavity and strong log-concavity: a review, Regularity Properties of Optimal Maps Between Nonconvex Domains in the Plane, Monge-Ampère equation on exterior domains, Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour, The engulfing property for sections of convex functions on the Heisenberg group and the associated quasi-distance, Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group, Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case, Riemannian metrics on convex sets with applications to Poincaré and log-Sobolev inequalities, Boundary Hölder gradient estimates for the Monge-Ampère equation, Prescribing capacitary curvature measures on planar convex domains, \(C^ 2\) a priori estimates for degenerate Monge-Ampère equations, Lipschitz estimates for commutators of singular integral operators associated with the sections, Unnamed Item, On Monge–Ampère Type Equations and Applications, On the \(W^{2,1+\varepsilon }\)-estimates for the Monge-Ampère equation and related real analysis, Partial \(W^{2,p}\) regularity for optimal transport maps, Boundary \(\varepsilon\)-regularity in optimal transportation, The Regularity of Mappings with a Convex Potential, Some new estimates for the complex Monge-Ampère equation, Free boundaries in optimal transport and Monge-Ampère obstacle problems, On the weak\(*\) convergence in \(H_{\mathcal{F}}^1(\mathbb{R}^n)\), Gradient estimates for potentials of invertible gradient-mappings on the sphere, Continuity and injectivity of optimal maps, Local regularity result for an optimal transportation problem with rough measures in the plane, Regularity of optimal maps on the sphere: the quadratic cost and the reflector antenna, The engulfing property from a convex analysis viewpoint, Boundedness of Monge-Ampère singular integral operators acting on Hardy spaces and their duals, Stability of flows associated to gradient vector fields and convergence of iterated transport maps, Variations of a class of Monge-Ampère-type functionals and their applications, Interior \(C^{1,\alpha}\) regularity for the linearized Monge-Ampère equation with VMO type coefficients, The \(L_p\) dual Minkowski problem and related parabolic flows, Note on an eigenvalue problem with applications to a Minkowski type regularity problem in \(\mathbb{R}^n\), On Monge-Ampère equations with homogenous right-hand sides, REGULARITY OF MONGE–AMPÈRE EQUATIONS IN OPTIMAL TRANSPORTATION, Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations, Hölder regularity of optimal mappings in optimal transportation, A mean-value inequality for non-negative solutions to the linearized Monge-Ampère equation, The \(L_p\) Minkowski problem for torsion, On the continuity of the solutions to the $L_p$ capacitary Minkowski problem, A Newton div-curl least-squares finite element method for the elliptic Monge-Ampère equation, The \(L _p\) capacitary Minkowski problem for polytopes, Least action principles for incompressible flows and geodesics between shapes, Geometric properties of the sections of solutions to the Monge-Ampère equation, A note on the engulfing property and the $\Gamma ^{1+ \alpha }$-regularity of convex functions in Carnot groups, 𝑊^{{}2,𝑝}–estimates for the linearized Monge–Ampère equation, The Lp Minkowski problem for q-capacity, On the regularity of the polar factorization for time dependent maps, The L_p Minkowski problem for the electrostatic p-capacity for $p\ge n$, On geometric characterizations for Monge-Ampère doubling measures., Harnack inequality for the linearized parabolic Monge-Ampère equation, The logarithmic capacitary Minkowski problem for polytopes, Partial regularity for optimal transport maps, On the ${\mathbb H}$-cone-functions for H-convex sets, A new $L^\infty$ estimate in optimal mass transport, C^{1,\alpha} Regularity of convex hypersurfaces with prescribed curvature measures, Regularity properties of monotone measure-preserving maps, \textit{A priori} bounds, existence, and uniqueness of smooth solutions to an anisotropic \(L_p\) Minkowski problem for log-concave measure, A Reconstructed Discontinuous Approximation to Monge-Ampère Equation in Least Square Formulation, Inverse iteration for the Monge–Ampère eigenvalue problem, Fully nonlinear integro-differential equations with deforming kernels, Besov and H\xF6lder spaces on spaces of homogeneous type, Boundedness of Monge–Ampère singular integral operators on Besov spaces, ON THE MONGE–AMPÈRE EQUATION IN INFINITE DIMENSIONS, A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations, Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations, Interior second derivative estimates for solutions to the linearized Monge-Ampère equation, Monge–Ampère singular integral operators acting on Triebel–Lizorkin spaces, Boundary $C^{1,\alpha}$ regularity of an optimal transport problem with cost close to $-x\cdot y$, Obstructions to extension of Wasserstein distances for variable masses, Boundary Harnack inequality for the linearized Monge-Ampère equations and applications, Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations



Cites Work