Displaying similar documents to “Local Lipschitz continuity of solutions of non-linear elliptic differential-functional equations”

Continuity of solutions to a basic problem in the calculus of variations

Francis Clarke (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the problem of minimizing Ω F ( D u ( x ) ) d x over the functions u W 1 , 1 ( Ω ) that assume given boundary values φ on Γ : = Ω . The lagrangian F and the domain Ω are assumed convex. A new type of hypothesis on the boundary function φ is introduced: the (or upper) . This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary data (instead...

Non-Trapping sets and Huygens Principle

Dario Benedetto, Emanuele Caglioti, Roberto Libero (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the evolution of a set Λ 2 according to the Huygens principle: the domain at time , Λ, is the set of the points whose distance from is lower than . We give some general results for this evolution, with particular care given to the behavior of the perimeter of the evoluted set as a function of time. We define a class of sets (non-trapping sets) for which the perimeter is a continuous function of , and we give an algorithm to approximate the evolution. Finally we restrict...

Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Adam Parusiński (2005)

Annales Polonici Mathematici

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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.

Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions

Hang Yu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients , in three dimensions, div ( μ ( u + u t ) ) + ( λ div u ) + V u = 0 where and are Lipschitz continuous and . The method is based on the Carleman estimate with polynomial weights for the Lamé operator.

New convexity conditions in the calculus of variations and compensated compactness theory

Krzysztof Chełmiński, Agnieszka Kałamajska (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the lower semicontinuous functional of the form I f ( u ) = Ω f ( u ) d x where satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar's -convexity condition for the integrand extends to the new geometric conditions satisfied on four dimensional symplexes. Similar conditions on three dimensional symplexes were recently obtained by the second author. New conditions...