Search results for "Overdetermined system"
showing 5 items of 15 documents
A note on an overdetermined problem for the capacitary potential
2016
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.
A Remark on an Overdetermined Problem in Riemannian Geometry
2016
Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let \(\varOmega \subset M\) be a bounded domain, with \(O \in \varOmega \), and consider the problem \(\varDelta _p u = -1\ \mathrm{in}\ \varOmega \) with \(u=0\ \mathrm{on}\ \partial \varOmega \), where \(\varDelta _p\) is the p-Laplacian of g. We prove that if the normal derivative \(\partial _{\nu }u\) of u along the boundary of \(\varOmega \) is a function of d satisfying suitable conditions, then \(\varOmega \) must be a geodesic ball. In particular, our result applies to open balls of \(\mathbb {R}^n\) equipped with a rotationally symmetric metr…
Estimating intrinsic image from successive images by solving underdetermined and overdetermined systems of the dichromatic model
2020
International audience; Estimating an intrinsic image from a sequence of successive images taken from an object at different angles of illumination can be used in various applications such as objects recognition, color classification, and the like; because, in so doing, it can provide more visual information. Meanwhile, according to the well-known dichromatic model, each image can be considered a linear combination of three components, including intrinsic image, shading factor, and specularity. In this study, at first, two simple independent constrained and parallelized quadratic programming steps were used for computing values of the shading factor and the specularity of each successive of…
Some overdetermined problems related to the anisotropic capacity
2018
Abstract We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω ⊂ R N , with 1 p N . In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q = − ( p − 1 ) / ( N − p ) if and only if Ω is Wulff shape.
On Serrin’s overdetermined problem in space forms
2018
We consider Serrin’s overdetermined problem for the equation $$\Delta v + nK v = -\,1$$ in space forms, where K is the curvature of the space, and we prove a symmetry result by using a P-function approach. Our approach generalizes the one introduced by Weinberger to space forms and, as in the Euclidean case, it provides a short proof of the symmetry result which does not make use of the method of moving planes.