By Tracy Kompelien

ISBN-10: 159928507X

ISBN-13: 9781599285078

Publication annotation no longer on hand for this title.**Title: **2-D Shapes Are at the back of the Drapes!**Author: **Kompelien, Tracy**Publisher: **Abdo Group**Publication Date: **2006/09/01**Number of Pages: **24**Binding kind: **LIBRARY**Library of Congress: **2006012570

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**Extra info for 2-D Shapes Are Behind the Drapes!**

**Example text**

C. g. Buttazzo [127] that Theorem 2 has a converse Theorem 4. f2 x R' -> R+ be any Borel function. c. in L' (0, RN; µ) with respect to the weak* convergence and that F is not identically +oo. e. f2 and all u. E RN. n defined on some subclass of the class of smooth maps u : 1? C Rn - I[8N Definition 1. ) Lxn(gu,rl) for all admissible smooth functions u. Correspondingly, we say that the integrand f (x, u, G) is regular if there exists a positive constant v such that (3) f (x, u, G) > v jM(G) j for all admissible N x n-matrices G.

More precisely we have Theorem 2. Let r2 be a separable topology, so that in particular compact sets are also closed. Suppose that F is ri -coercive. Then (i) F is 'r2-coercive (ii) We have (4) F(r2)-F(y) = inf{F(-ri)-F(x) +oo { I j(x) = y} if y E j(Yi) ifyEY2\j(Yi). Proof. For any compact set K C Y1, j(K) is compact hence closed, j(K) _ j(K). Fort ER set Bt := {x E Yl I F(x) < t} . By the assumptions Bt is relatively compact. Hence i(Bt) = {y E Y2 I F(y) < t} is relatively compact, too. In fact i(Bt) C i(Bt) = i(Bt) which is closed and compact.

C. in L' (0, RN; µ) with respect to the weak* convergence and that F is not identically +oo. e. f2 and all u. E RN. n defined on some subclass of the class of smooth maps u : 1? C Rn - I[8N Definition 1. ) Lxn(gu,rl) for all admissible smooth functions u. Correspondingly, we say that the integrand f (x, u, G) is regular if there exists a positive constant v such that (3) f (x, u, G) > v jM(G) j for all admissible N x n-matrices G. 24 1. F-energies are well identified as Cartesian currents. F(u, Si); we shall then study in the next section properties, as semicontinuity with respect to weak convergence of Cartesian currents, of such an extension.

### 2-D Shapes Are Behind the Drapes! by Tracy Kompelien

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