Advances in Differential Equations

On Serrin's symmetry result in nonsmooth domains and its applications

Juraj Földes

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The paper investigates overdetermined fully nonlinear problems on nonsmooth domains. Under natural regularity assumptions on solutions it is shown that overdetermined problems on reflectionally symmetric, bounded domains can have positive solutions only if the domain is a ball. These results are extensions of results of Serrin, who proved this statement for smooth solutions on smooth domains. The results for overdetermined problems are applied to a study of Dirichlet problems, specifically to the question when a nonnegative solution is positive or zero everywhere. As a consequence, an extension of symmetry results of Gidas--Ni--Nirenberg to nonnegative solutions is obtained.

Article information

Adv. Differential Equations, Volume 18, Number 5/6 (2013), 523-548.

First available in Project Euclid: 14 March 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35N25: Overdetermined boundary value problems 35B06: Symmetries, invariants, etc. 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations 35B09: Positive solutions


Földes, Juraj. On Serrin's symmetry result in nonsmooth domains and its applications. Adv. Differential Equations 18 (2013), no. 5/6, 523--548.

Export citation