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Sayfa 734
Application of the contraction principle . First , let us estimate the norms of w and
F ( w ) . The inequality ( 5 . 2 ) gives us ( 5 . 19 ) W ( x ) < 1 x E DA if A is
sufficiently large , and ( 5 . 20 ) | | Wlle 5 const / AP , for arbitrarily chosen positive
u and B ...
Application of the contraction principle . First , let us estimate the norms of w and
F ( w ) . The inequality ( 5 . 2 ) gives us ( 5 . 19 ) W ( x ) < 1 x E DA if A is
sufficiently large , and ( 5 . 20 ) | | Wlle 5 const / AP , for arbitrarily chosen positive
u and B ...
Sayfa 736
Multiplying ( 5 . 34 ) by ( xly and taking the maximum , we get ( 5 . 35 ) | | F ( W ) lly
< const · | C 12 . 2017 · max \ x | p + 2e47 ( A - \ Imxl ) . Here we used the
inequality 1x1 < const . Im xl . If A > ( y + 2 ) / 41 , then maximum in the right side
of ( 5 .
Multiplying ( 5 . 34 ) by ( xly and taking the maximum , we get ( 5 . 35 ) | | F ( W ) lly
< const · | C 12 . 2017 · max \ x | p + 2e47 ( A - \ Imxl ) . Here we used the
inequality 1x1 < const . Im xl . If A > ( y + 2 ) / 41 , then maximum in the right side
of ( 5 .
Sayfa 744
if A is large enough . We took into account that for any k > 0 byl•lxlk se - 26 ) Imx |
/ m • 1xk < const · Ake - 1A 1 . Similarly , if & 1 , $ 2 € B , then \ F ( $ 1 ) ( x , y ) – F (
52 ) ( x , y ) | | s const . ly | - } | el | y | 4 max { \ P ( 81 ) ( x , y ) ] , \ P ( 82 ) ( x , y ) ...
if A is large enough . We took into account that for any k > 0 byl•lxlk se - 26 ) Imx |
/ m • 1xk < const · Ake - 1A 1 . Similarly , if & 1 , $ 2 € B , then \ F ( $ 1 ) ( x , y ) – F (
52 ) ( x , y ) | | s const . ly | - } | el | y | 4 max { \ P ( 81 ) ( x , y ) ] , \ P ( 82 ) ( x , y ) ...
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İçindekiler
HADAMARDS CONJECTURE | 634 |
Necessary facts about Sobolev spaces | 643 |
Elliptic differential inequalities | 655 |
Telif Hakkı | |
5 diğer bölüm gösterilmiyor
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
According algebra analytic apply assertion assume asymptotic Banach space boundary bounded called closed complete condition cone connected Consequently consider const constant construction contains continuous corresponding cubes defined definition denote depend derivatives described determined differential direct domain eigenvalues element English transl equality equation equivalent estimate example exists extension fact field finite fixed follows formula function Further given gives hence holds implies inequality integral introduce lattice Lemma limit linear mapping Math Mathematical matrix means measure multiplicity norm obtained Obviously operator pair particular perturbation polynomial positive possible present principle problem Proof properties Proposition proved reduced relation remains Remark representation respect satisfies scattering side smooth solution space spectral spectrum subspace sufficiently Suppose Theorem theory unique valid vector zero