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Titlebook: Geometric Partial Differential Equations; Antonin Chambolle,Matteo Novaga,Enrico Valdinoci Conference proceedings 2013 Scuola Normale Supe

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Digitalisierung der Gesundheitswirtschaftmedia. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we investigate its strict convexity and differentiability properties.
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Bernhard Nett,Bernd Remmele,Britta Schinzelflat domain of ℝ.. More precisely, we prove that given an exponent α ∈ (0,1), there exists an ε > 0 such that the solution . to the previous system is locally Hölder continuous provided that Ω is (ε, ..)-Reifenberg-flat. The proof is based on Alt-Caffarelli-Friedman’s monotonicity formula and Morrey-Campanato theorem.
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On the structure of phase transition maps for three or more coexisting phases,For symmetric W’s the main issues have been resolved, and we summarize them here. Next we recall the De Giorgi conjecture in the scalar case, and we point to a Bernstein type theorem that appears appropriate for (1.1). Finally we state a result on the hierarchical structure of the equivariant solutions.
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The nonlinear multidomain model: a new formal asymptotic analysis,ult formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the . original anisotropies.
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Homogenization with oscillatory Neumann boundary data in general domain,is oscillatory. Our result on the Neumann problem is the nonlinear version of the classical result in [4] for divergence-form operators with co-normal boundary data. We also discuss the Dirichlet boundary problem.
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