共查询到20条相似文献,搜索用时 5 毫秒
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V. G. Dubrovsky A. V. Topovsky M. Yu. Basalaev 《Theoretical and Mathematical Physics》2011,167(3):725-739
We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik-Veselov-Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup-Kupershmidt and Sawada-Kotera equations, constructed using the Zakharov-Manakov \(\bar \partial \)-dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik-Veselov-Novikov equation. 相似文献
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Steven G. Krantz 《manuscripta mathematica》1978,24(4):351-378
An intrinsic definition of Lipschitz classes in terms of vector fields on man-ifolds is provided and it is shown that it is locally equivalent with a more classical definition. A finer result is then proved for strongly pseudo-convex CR manifolds and applications of the theorems are given to smoothness of holomorphic functions and estimates for the \(\bar \partial \) and \(\bar \partial _b \) . equations. 相似文献
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Bo Berndtsson 《Journal of Geometric Analysis》1997,7(2):195-215
This paper concernsL ∞-variants of Hörmanders weightedL 2-estimates for the $\bar \partial - equation$ . In particular, we discuss a conjecture concerning suchL ∞-estimates which is related to the corona problem in the ball, and show a weaker version of this conjecture. The proof uses a refinedL 2-estimate for the canonical solution to the $\bar \partial - equation$ . An alternative approach based on von Neumann’s Minimax theorem is also given. 相似文献
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S. Saber 《Mathematica Slovaca》2013,63(3):521-530
For a q-pseudoconvex domain Ω in ? n , 1 ≤ q ≤ n, with Lipschitz boundary, we solve the $\bar \partial $ -problem with exact support in Ω. Moreover, we solve the $\bar \partial $ -problem with solutions smooth up to the boundary over Ω provided that it has smooth boundary. Applications are given to the solvability of the tangential Cauchy-Riemann equations on the boundary. 相似文献
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Steven Bell 《Journal of Geometric Analysis》1993,3(3):195-224
We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz
0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported
away fromz
0 cannot vanish to infinite order atz
0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the
problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in
several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection
and kernel in planar domains.
Research supported by NSF Grant DMS-8922810. 相似文献
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It is shown that every solution to the equation $
X\bar X = \bar XX
$
X\bar X = \bar XX
can be reduced by a real orthogonal similarity transformation to a block triangular form with diagonal blocks of orders one
and two. If the solution X is a normal matrix, then its block triangular form is actually a block diagonal. In this case, the form of the diagonal blocks
is found, yielding new proof of the recent results of Goodson and Horn. 相似文献