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85 sonuçtan 1-3 arası sonuçlar
Sayfa 643
Remark . We remark that Theorem 5 . 1 can fail without the assumption that cos (
K ) > 0 . 82 . NECESSARY FACTS ABOUT SOBOLEV SPACES Let 12c R " be a
bounded open set , let p > 1 be a real number , and let 1 2 0 be an integer .
Remark . We remark that Theorem 5 . 1 can fail without the assumption that cos (
K ) > 0 . 82 . NECESSARY FACTS ABOUT SOBOLEV SPACES Let 12c R " be a
bounded open set , let p > 1 be a real number , and let 1 2 0 be an integer .
Sayfa 1073
Remark 5 . 6 . 1 ) The assertions of Theorem 5 . 5 are “ uniform ” with respect to a
> 0 on each sufficiently small interval [ 11 , 22 ] C ( 0 , 00 ) . 2 ) For q = Ego
Theorem 5 . 5 enables us to follow the motion of the spectrum of So ( a ) as the ...
Remark 5 . 6 . 1 ) The assertions of Theorem 5 . 5 are “ uniform ” with respect to a
> 0 on each sufficiently small interval [ 11 , 22 ] C ( 0 , 00 ) . 2 ) For q = Ego
Theorem 5 . 5 enables us to follow the motion of the spectrum of So ( a ) as the ...
Sayfa 1160
3 ) , ( 3 . 6 ) , and ( 3 . 8 ) need to be satisfied only for those values of the levels k
and k for which ess sup ( ( u – k ) + , QnQr ) < 8 , ( u – k ) + = 0 on S = QnSt , and
ess sup ( ( û – k ) + , 2nQr ) < d , ( û – k ) + = 0 on S = On St respectively . Remark
.
3 ) , ( 3 . 6 ) , and ( 3 . 8 ) need to be satisfied only for those values of the levels k
and k for which ess sup ( ( u – k ) + , QnQr ) < 8 , ( u – k ) + = 0 on S = QnSt , and
ess sup ( ( û – k ) + , 2nQr ) < d , ( û – k ) + = 0 on S = On St respectively . Remark
.
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İçindekiler
HADAMARDS CONJECTURE | 634 |
Necessary facts about Sobolev spaces | 643 |
Elliptic differential inequalities | 655 |
Telif Hakkı | |
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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