An Introduction to Lorentz Surfaces (De Gruyter Expositions by Tilla Weinstein

By Tilla Weinstein

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Example text

Dual System, Green Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Lemma . . . . . . .

1(3) Here we set the index s = 2 in Eq. 24). 67) where again [φ, φt , ϑ] solve the homogeneous system Eq. 9). Using the relation Eq. 65), we have T (1 − ) 1 ˚ 2φ h(t) A 0 2 dt L2( ) T ≤C h(t) + 0 T ≤ CT 2 [h (t)]2 h(t) φt 2 L2( ) φt 2 L2( ) + ϑ 2 L2( ) dt. φt 2 L2( ) + ϑ 2 L2( ) dt, 0 + ϑ 2 L2( ) dt This then gives T 0 T h(t)E(t) dt ≤ C T 2 0 whence we obtain the inequality Eq. 67). From here, we can use the usual algorithmic argument 3 so as to have Emin (T ) = O(T − 2 ). 1(3). References [1] P.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Part II: Boundary Control [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . .

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