We first prove De Giorgi type level estimates for functions in W-1,W-t(Omega), Omega subset of R-N, with t > N >= 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 W-1,W-2(Omega). 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.

Maximum principle for higher order operators in general domains

Daniele Cassani
;
2021-01-01

Abstract

We first prove De Giorgi type level estimates for functions in W-1,W-t(Omega), Omega subset of R-N, with t > N >= 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 W-1,W-2(Omega). 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.
2021
2021
Harnack's inequality, Higher order PDEs; Polyharmonic operators; Positivity preserving property
Cassani, Daniele; Tarsia, Antonio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2120460
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