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Sayfa 655
ELLIPTIC DIFFERENTIAL INEQUALITIES A test function de C ( 12 ) is said to be
positive if y ( x ) > 0 for all xe $ 2 . A distribution AE D ' ( 12 ) is said to be positive
if ( 1 , 0 ) > 0 for any positive test function de CO ( 12 ) . The positivity of a will be ...
ELLIPTIC DIFFERENTIAL INEQUALITIES A test function de C ( 12 ) is said to be
positive if y ( x ) > 0 for all xe $ 2 . A distribution AE D ' ( 12 ) is said to be positive
if ( 1 , 0 ) > 0 for any positive test function de CO ( 12 ) . The positivity of a will be ...
Sayfa 656
The set of positive distributions is a cone in the space of distributions of order
zero [ 25 ] . Therefore , for any positive distribution A there exists a unique
positive Borel measure un such that ( 4 , 0 ) = s odun for all Q E COO ( 12 ) . A
distribution u ...
The set of positive distributions is a cone in the space of distributions of order
zero [ 25 ] . Therefore , for any positive distribution A there exists a unique
positive Borel measure un such that ( 4 , 0 ) = s odun for all Q E COO ( 12 ) . A
distribution u ...
Sayfa 1072
2 ) holds , and the ASM S is an operator of negative ( positive ) type . Proof . It
suffices to verify that the eigenvalues of the operator ( 5 . 1 ) do not accumulate at
zero from the right ( left ) . It can again be assumed that Q = 1 ( Q = - 1 ) .
2 ) holds , and the ASM S is an operator of negative ( positive ) type . Proof . It
suffices to verify that the eigenvalues of the operator ( 5 . 1 ) do not accumulate at
zero from the right ( left ) . It can again be assumed that Q = 1 ( Q = - 1 ) .
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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