Abstract
We consider an overdetermined problem associated to an inhomogeneous
infinity-Laplace equation. More precisely, the domain of the problem
is required to contain a given compact set K of positive reach, and
the boundary of the domain must lie within the reach of K. We look
for a solution vanishing at the boundary and such that the outer
derivative depends only on the distance from K. We prove that if the
boundary gradient grows fast enough with respect to such distance
(faster than the distance raised to
Dedicated to Gérard A. Philippin, a source of inspiration and encouragement
Funding statement: The author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). This work was partially supported by the research project “Integro-differential Equations and Non-Local Problems”, funded by Fondazione di Sardegna (2017).
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Articles in the same Issue
- Frontmatter
- An overdetermined problem for the infinity-Laplacian around a set of positive reach
- Tangential derivatives and higher-order regularizing properties of the double layer heat potential
- A uniqueness result for differential pencils with discontinuities from interior spectral data
Articles in the same Issue
- Frontmatter
- An overdetermined problem for the infinity-Laplacian around a set of positive reach
- Tangential derivatives and higher-order regularizing properties of the double layer heat potential
- A uniqueness result for differential pencils with discontinuities from interior spectral data