On some Lp-estimates for solutions of elliptic equations in unbounded domains

Title:

On some Lp-estimates for solutions of elliptic equations in unbounded domains

Creator:

Monsurrò, Sara and Transirico, Maria

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f51f253a-7f6c-45d3-aa60-36af144a3c83
uuid:f51f253a-7f6c-45d3-aa60-36af144a3c83
doi:10.21136/MB.2015.144466

Subject:

elliptic equation, discontinuous coefficient, and a priori bound

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this review article we present an overview on some a priori estimates in L p , p > 1, recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two L p -bounds, p > 2, for the solution of the associated Dirichlet problem, obtained in correspondence with two different sign assumptions. Then, putting together the above mentioned bounds and using a duality argument, we extend the estimate also to the case 1 < p < 2, for each sign assumption, and for a data in L p ∩ L 2 .

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

507-515

Source:

Mathematica bohemica | 2015 Volume:140 | Number:4

Harvested from:

CDK

Metadata only:

false