Some problems in automata theory which depend on the models of set theory

Olivier Finkel

Displaying similar documents to “Some problems in automata theory which depend on the models of set theory”

Asymmetric heteroclinic double layers

Michelle Schatzman (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let be a non-negative function of class C from $^{2}$ to , which vanishes exactly at two points and . Let (, ) be the set of functions of a real variable which tend to at -∞ and to at +∞ and whose one dimensional energy $E_{1} (v) = \int_{[W (v) + {| v^{'} |}^{2} / 2]} x$ is finite. Assume that there exist two isolated minimizers and of the energy over (, ). Under a mild coercivity condition on the potential and a generic spectral condition on the linearization...

Higher-order phase transitions with line-tension effect

Bernardo Galvão-Sousa (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by...

A new (div)-conforming -interpolation operator in two dimensions

Alexei Bespalov, Norbert Heuer (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we construct a new (div)-conforming projection-based -interpolation operator that assumes only () $\cap$ $\tilde{𝐇}$ (div, )-regularity ( > 0) on the reference element (either triangle or square) . We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space $\tilde{𝐇}$ (div, ), which is closely...