A new method of proving a priori bounds for superlinear elliptic PDE
Analysis of PDEs
2019-04-16 v2
Abstract
We describe a new method of proving a priori bounds for positive supersolutions and solutions of superlinear elliptic PDE, based on global weak Harnack inequalities and a quantitative Hopf lemma. Novel results based on the method include: (i) equations without a boundary condition on the whole boundary; (ii) equations with nonlinearities which do not have precise growth at infinity; (iii) systems of inequalities with opposite sign.
Keywords
Cite
@article{arxiv.1904.03245,
title = {A new method of proving a priori bounds for superlinear elliptic PDE},
author = {Boyan Sirakov},
journal= {arXiv preprint arXiv:1904.03245},
year = {2019}
}
Comments
14 pages, some simple corrections included in this version