Upper bounds for parabolic equations and the Landau equation

By Luis Silvestre. 2015

63 citations recorded by the source corpus.

We consider a parabolic equation in nondivergence form, defined in the full space $[0,\infty) \times \mathbb R^d$, with a power nonlinearity as the right hand side. We obtain an upper bound for the solution in terms of a weighted control in $L^p$. This upper bound is applied to the homogeneous Landau equation with moderately soft potentials. We obtain an estimate in $L^\infty(\mathbb R^d)$ for the solution of the Landau equation, for positive time, which depends only on the mass, energy and entropy of the initial data.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b11449dd7d14f3dbb4b10e873521547230527d21

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, background): “Let us also mention that in [55], Silvestre derives an L ∞ bound on the spatially homogeneous solutions for soft potentials without relying on energy methods (which implies as well the smoothing by standard parabolic techniques).”