Download PDF by Gianni Dal Maso (auth.): An Introduction to Γ-Convergence

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  • March 28, 2018
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={ f(x,~) , if x ¢ B, 0, if x E B, R be the corresponding integral functional, defined by G(u) = io9(X,DU)dX. 8) we have Fh + cc ~ G for every h ~ k. 2). 5) can be obtained by taking the limit as c tends to O. 0 Chapter 6 Some Properties of r-limits In this chapter we study some properties of r -limits and K-limits which hold on every topological space X.

Then the minimum problem min(f f(x,Du(x))dx+ uEK in f g(x,u(x))dx) in has a solution. e. e. x E n the function g(x,·) is strictly convex on R. 6. The only difference is in the proof of the coerciveness of the functional F + G + X K , because now from (ii) and (iv) we get only the inequality Proof. (F+G+XK)(u) ~ Co In/DU/PdX+C1 In/U/PdX-b, where b = /lao/lLl(n) + /lad/LI(n) and Cl now may be negative. 3). 15. 20. 9. Assume that p > 1, meas(n) < +00, and that f satisfies (i) and (ii), with Co > o.

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An Introduction to Γ-Convergence by Gianni Dal Maso (auth.)


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