Displaying similar documents to “On the Γ -convergence of Laplace-Beltrami operators in the plane.”

On two-scale convergence and related sequential compactness topics

Anders Holmbom, Jeanette Silfver, Nils Svanstedt, Niklas Wellander (2006)

Applications of Mathematics

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A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L 2 ( Ω ) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.

On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation

Petr Harasim (2008)

Applications of Mathematics

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We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient. ...

On weak Hessian determinants

Luigi D'Onofrio, Flavia Giannetti, Luigi Greco (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.

Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach

Fabio Paronetto (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations ∂ t ( r h u ) - div ( a h · D u ) with r h ( x , t ) ≥ 0 , r h ∈ L ∞ ( Ω × ( 0 , T ) ) . The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain -convergence for elliptic operators ( r h ≡ 0 ) , -convergence for parabolic operators ( r h ≡ 1 ) , singular perturbations of an elliptic operator ( a h ≡ a and r h → r , possibly r ≡ 0 ) .