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Uniqueness results for the Minkowski problem extended to hedgehogs

100%
Martinez-Maure Y.
Open Mathematics
|
2012
|
tom 10
|
nr 2
440-450
EN
The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere $\mathbb{S}^n $ of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.
2
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On a generalized Stokes problem

100%
Mácha V.
Open Mathematics
|
2011
|
tom 9
|
nr 4
874-887
EN
We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.
3
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Global and exponential attractors for a Caginalp type phase-field problem

81%
Bangola B.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1651-1676
EN
We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
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