Overdetermined problems for p-Laplace and generalized Monge–Ampére equations

Abstract

We investigate overdetermined problems for p-Laplace and generalized Monge–Ampére equations. By using the theory of domain derivative, we find duality results and characterization of the overdetermined boundary conditions via minimization of suitable functionals with respect to the domain.

COMMUNICATED BY:

• D. Repovš

Keywords:

• Overdetermined problems
• domain derivative
• duality results
• domain functionals
• p-Laplace equations
• generalized Monge–Ampére equations

AMS Subject Classifications:

• 35N25
• 35A23
• 35J96
• 47J20
• 52A40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Y. Liu is partly supported by the Natural Science Foundation of Jiangsu Province [grant number BK20200249].