Quasi-Harnack inequality
| Autor: | Ovidiu Savin, Daniela De Silva |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Scale (ratio) General Mathematics Infinitesimal Type (model theory) 01 natural sciences Homogenization (chemistry) 010101 applied mathematics Mathematics - Analysis of PDEs Quadratic equation FOS: Mathematics 0101 mathematics Analysis of PDEs (math.AP) Mathematics Harnack's inequality |
| Zdroj: | American Journal of Mathematics. 143:307-331 |
| ISSN: | 1080-6377 |
| DOI: | 10.1353/ajm.2021.0001 |
| Popis: | In this paper we obtain some extensions of the classical Krylov-Safonov Harnack inequality. The novelty is that we consider functions that do not necessarily satisfy an infinitesimal equation but rather exhibit a two-scale behavior. We require that at scale larger than some $r_0>0$ (small) the functions satisfy the comparison principle with a standard family of quadratic polynomials, while at scale $r_0$ they satisfy a Weak Harnack type estimate. We also give several applications of the main result in very different settings such as discrete difference equations, nonlocal equations, homogenization and the quasi-minimal surfaces of Almgren. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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