We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on L^1 comparison) between solutions to an elliptic partial differential equation on a smooth bounded set Ω with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as Ω. This includes for instance mixed problems where Dirichlet boundary conditions are prescribed on part of the boundary, while Robin boundary conditions are prescribed on its complement.
Sharp estimates for solutions to elliptic problems with mixed boundary conditions / Alvino, Angelo; Chiacchio, Francesco; Nitsch, Carlo; Trombetti, Cristina. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 1776-3371. - 152:9(2021), pp. 251-261. [10.1016/j.matpur.2020.12.003]
Sharp estimates for solutions to elliptic problems with mixed boundary conditions
Angelo Alvino;Francesco Chiacchio;Carlo Nitsch;Cristina Trombetti
2021
Abstract
We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on L^1 comparison) between solutions to an elliptic partial differential equation on a smooth bounded set Ω with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as Ω. This includes for instance mixed problems where Dirichlet boundary conditions are prescribed on part of the boundary, while Robin boundary conditions are prescribed on its complement.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
