Regularity of the Monge-Ampère equation in Besov's spaces

DOI10.1007/s00526-013-0617-5zbMath1290.35098arXiv1203.3457OpenAlexW2061160294WikidataQ115387433 ScholiaQ115387433MaRDI QIDQ2445461

Sergey Yu. Tikhonov, Alexander V. Kolesnikov

Publication date: 14 April 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3457

zbMATH Keywords

regularityMonge-Ampère equationoptimal transportation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60)

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Regularity estimates for the parabolic \(p (x, t)\)-Laplacian equation in Besov spaces ⋮ Besov estimates for weak solutions of a class of quasilinear parabolic equations with general growth ⋮ Besov estimates for weak solutions of the parabolic \(p\)-Laplacian equations ⋮ Besov regularity estimates for the elliptic \(p(x)\)-Laplacian equation with the logarithmic growth ⋮ On continuity equations in infinite dimensions with non-Gaussian reference measure ⋮ Besov estimates for the weak solutions of a class of quasilinear elliptic equations

Cites Work

• Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures
• Sobolev regularity for the Monge-Ampère equation in the Wiener space
• On the mean oscillation of the Hessian of solutions to the Monge-Ampère equation
• Entropy-rigidity of locally symmetric spaces of negative curvature
• Convex measures on locally convex spaces
• A convexity principle for interacting gases
• Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Global 𝑊^{2,𝑝} estimates for the Monge-Ampère equation
• Some Counterexamples to the Regularity of Monge-Ampere Equations
• The Monge-Kantorovich problem: achievements, connections, and perspectives
• On limiting embeddings of Besov spaces
• Optimal Transport
• The Monge-Ampère equation
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