Maximum principle for higher order operators in general domains
We first prove De Giorgi type level estimates for functions in W1,t(Ω), Ω⊂RN$ \Omega\subset{\mathbb R}^N $, with t>N≥2$ t \gt N\geq 2 $. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtai...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/368a5e7b8ef14ed7b9353e188f331605 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | We first prove De Giorgi type level estimates for functions in W1,t(Ω), Ω⊂RN$ \Omega\subset{\mathbb R}^N $, with t>N≥2$ t \gt N\geq 2 $. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtained in Di Benedetto–Trudinger [10] for functions in W1,2(Ω). As a consequence, we prove the validity of the strong maximum principle for uniformly elliptic operators of any even order, in fairly general domains in dimension two and three, provided second order derivatives are taken into account. |
|---|