Pointwise estimates via parabolic potentials for a class of doubly nonlinear parabolic equations with measure data

Autor: Stefan Sturm
Rok vydání: 2018
Předmět:
Zdroj: manuscripta mathematica. 157:295-322
ISSN: 1432-1785
0025-2611
DOI: 10.1007/s00229-018-1014-3
Popis: On a cylindrical domain $$E_T$$ , we consider doubly nonlinear parabolic equations, whose prototype is $$\partial _t u - \mathrm{div}(|u|^{m-1}|Du|^{p-2}Du) = \mu ,$$ where $$\mu $$ is a non-negative Radon measure having finite total mass $$\mu (E_T)$$ . The central objective is to establish pointwise estimates for weak solutions in terms of nonlinear parabolic potentials in the doubly degenerate case $$(p\ge 2, m>1)$$ . Moreover, we will prove the sharpness of the estimates by giving an optimal Lorentz space criterion regarding the local uniform boundedness of weak solutions and by comparing them to the decay of the Barenblatt solution.
Databáze: OpenAIRE
Externí odkaz: