On the Sobolev space of functions with derivative of logarithmic order

DOI10.1515/anona-2020-0027zbMath1437.46038arXiv1807.03262OpenAlexW2969347612WikidataQ127341618 ScholiaQ127341618MaRDI QIDQ2008883

Yanyan Li

Publication date: 26 November 2019

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.03262

zbMATH Keywords

Sobolev spacesderivative of logarithmic order

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and differentiation questions (26B05)

Related Items

Strong convergence of the vorticity for the 2D Euler equations in the inviscid limit ⋮ Advection diffusion equations with Sobolev velocity field ⋮ Fractional Sobolev inequalities revisited: the maximal function approach ⋮ Endpoint Sobolev theory for the Muskat equation ⋮ Restricting Riesz-logarithmic-Besov potentials ⋮ The logarithmic Sobolev capacity ⋮ Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts ⋮ On the Cauchy problem for the Muskat equation. II: Critical initial data ⋮ A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms ⋮ Global existence and blowup in infinite time for a fourth order wave equation with damping and logarithmic strain terms ⋮ On the Cauchy problem for the Muskat equation with non-Lipschitz initial data ⋮ New Brezis-van Schaftingen-Yung-Sobolev type inequalities connected with maximal inequalities and one parameter families of operators ⋮ Anomalous dissipation in passive scalar transport ⋮ Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields ⋮ Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
• On Besov spaces of logarithmic smoothness and Lipschitz spaces
• A quantitative isoperimetric inequality for fractional perimeters
• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Sharp embeddings of Besov spaces involving only logarithmic smoothness
• Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor
• Generalized Gagliardo-Nirenberg inequalities using Lorentz spaces, BMO, Hölder spaces and fractional Sobolev spaces
• Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and \(\mathrm{RCD}(K,\infty)\) spaces
• Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
• Elliptic Systems, Singular Sets and Dini Continuity
• Nonsmooth calculus
• Estimates and regularity results for the DiPerna-Lions flow
• A new approach to bounds on mixing

This page was built for publication: On the Sobolev space of functions with derivative of logarithmic order