Emergence of exponentially weighted Lp-norms and Sobolev regularity for the Boltzmann equation

DOI10.1080/03605302.2018.1554676OpenAlexW2908675796MaRDI QIDQ5379273

Ricardo J. Alonso

Publication date: 28 May 2019

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2018.1554676

zbMATH Keywords

fractional diffusionsDe Giorgi level set methodnon cutoff Boltzmann

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) Boltzmann equations (35Q20)

Related Items (7)

On the Cauchy problem for Boltzmann equation modeling a polyatomic gas ⋮ About the Landau-Fermi-Dirac equation with moderately soft potentials ⋮ Local Well-Posedness for the Boltzmann Equation with Very Soft Potential and Polynomially Decaying Initial Data ⋮ De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation ⋮ Regularity estimates and open problems in kinetic equations ⋮ About the use of entropy production for the Landau-Fermi-Dirac equation ⋮ On Pointwise Exponentially Weighted Estimates for the Boltzmann Equation

Cites Work

• Unnamed Item
• Unnamed Item
• A new regularization mechanism for the Boltzmann equation without cut-off
• Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff
• Smoothing estimates for Boltzmann equation with full-range interactions: spatially homogeneous case
• The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• Propagation of \(L^1\) and \(L^\infty \) Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann equation
• Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
• A proof of the smoothing properties of the positive part of Boltzmann's kernel
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• Entropy dissipation and moment production for the Boltzmann equation
• Entropy dissipation and long-range interactions
• Propagation of stretched exponential moments for the Kac equation and Boltzmann equation with Maxwell molecules
• About \(L^p\) estimates for the spatially homogeneous Boltzmann equation
• The weak Harnack inequality for the Boltzmann equation without cut-off
• On strong convergence to equilibrium for the Boltzmann equation with soft potentials
• Global classical solutions of the Boltzmann equation without angular cut-off
• Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
• On Mittag-Leffler Moments for the Boltzmann Equation for Hard Potentials Without Cutoff
• On Pointwise Exponentially Weighted Estimates for the Boltzmann Equation

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