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Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension

Jan Prüss, Gieri Simonett (2009)

Banach Center Publications

The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.

Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).

Henrik Shahgholian (2003)

Revista Matemática Iberoamericana

Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 2), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N-dimension) and therefore its Hausdorff dimension is less than N. In particular the N-Lebesgue measure of the free boundary is zero for each t-level.

Anisotropic inverse problems and Carleman estimates

David Dos Santos Ferreira (2007/2008)

Séminaire Équations aux dérivées partielles

This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...

Anisotropic parabolic problems with slowly or rapidly growing terms

Agnieszka Świerczewska-Gwiazda (2014)

Colloquium Mathematicae

We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued, with growth conditions formulated with the help of an x-dependent N-function. The main novelty of the paper consists in the lack of any growth restrictions on the N-function combined with its anisotropic character, namely we allow the dependence on all the directions of the gradient, not only on its absolute value. This leads to using the notion of modular convergence and studying in detail...

Currently displaying 221 – 240 of 1900