Can I read Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation on EtoBox?

Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation by Matteo Bonforte; Razvan Gabriel Iagar; Juan Luis Vázquez is a Mathematics article available to read on EtoBox.

What is Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation about?

We study qualitative and quantitative properties of local weak solutions of the fast p-Laplacian equation, ∂ t u = p u, with 1 < p < 2. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of R n × [0, T ]. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion range, that is when 1 < p 2n/(n + 1). The boundedness results may be also extended to the limit case p = 1, while the positivity estimates cannot. We prove the existence as well as sharp asymptotic estimates for the so-called large solutions for any 1 < p < 2, and point out their main properties. We also prove a new local energy inequality for suitable norms of the gradients of the solutions. As a consequence, we prove that bounded local weak solutions are indeed local strong solutions, more precisely ∂ t u ∈ L 2 loc .

Who reads Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation?

Author

Matteo Bonforte; Razvan Gabriel Iagar; Juan Luis Vázquez

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)