Download PDF by Luigi Ambrosio (auth.), Antonio Bove, Daniele Del Santo,: Advances in Phase Space Analysis of Partial Differential

By Luigi Ambrosio (auth.), Antonio Bove, Daniele Del Santo, M.K. Venkatesha Murthy (eds.)

ISBN-10: 0817648607

ISBN-13: 9780817648602

This number of unique articles and surveys addresses the new advances in linear and nonlinear facets of the idea of partial differential equations.

Key issues include:

* Operators as "sums of squares" of actual and complicated vector fields: either analytic hypoellipticity and regularity for extraordinarily low regularity coefficients;

* Nonlinear evolution equations: Navier–Stokes process, Strichartz estimates for the wave equation, instability and the Zakharov equation and eikonals;

* neighborhood solvability: its reference to subellipticity, neighborhood solvability for structures of vector fields in Gevrey classes;

* Hyperbolic equations: the Cauchy challenge and a number of features, either confident and adverse results.

Graduate scholars at a number of degrees in addition to researchers in PDEs and comparable fields will locate this a superb resource.

List of contributors:

L. Ambrosio N. Lerner

H. Bahouri X. Lu

S. Berhanu J. Metcalfe

J.-M. Bony T. Nishitani

N. Dencker V. Petkov

S. Ervedoza J. Rauch

I. Gallagher M. Reissig

J. Hounie L. Stoyanov

E. Jannelli D. S. Tartakoff

K. Kajitani D. Tataru

A. Kurganov F. Treves

G. Zampieri

E. Zuazua

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Read Online or Download Advances in Phase Space Analysis of Partial Differential Equations: In Honor of Ferruccio Colombini's 60th Birthday PDF

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Additional resources for Advances in Phase Space Analysis of Partial Differential Equations: In Honor of Ferruccio Colombini's 60th Birthday

Sample text

There is also a similar arc J with z5 in its interior and we may assume that I and J are disjoint. But then this would contradict the injectivity of F on I ∪ J\{z4 , z5 } and so we must have F (z4 ) = F (z5 ). Hence F can be extended as a homeomorphism up to the part of the boundary of Ω that is disjoint from the one-dimensional orbits. It is also real analytic past all but a finite number of the points that do not lie in the one-dimensional orbits. Assume next that z0 ∈ ∂Ω ∩D ∩γ j for some j ≥ 1 and write, for simplicity of notation, γ j = Γ .

1 for the precise formulation). Section 3 is devoted to the proof of this result and Section 4 presents various examples. In Section 5, we show that for any smooth vector field, local solvability is a necessary and sufficient condition for the validity of the Rudin–Carleson property in arbitrary small neighborhoods of a point in an open set. In the final section we briefly discuss the relationship between the Rudin–Carleson theorem and the F. and M. Riesz theorem in the spirit of [B]. 2 Preliminaries and statement of the main result Let L = X + iY be a smooth vector field on an open set Ω in C where X and Y are real vector fields.

It is also real analytic past all but a finite number of the points that do not lie in the one-dimensional orbits. Assume next that z0 ∈ ∂Ω ∩D ∩γ j for some j ≥ 1 and write, for simplicity of notation, γ j = Γ . Write L = X + iY with X and Y real vector fields. Replacing L, if necessary, by a convenient nonvanishing multiple of L we may assume that Γ is a closed integral curve of X joining two points A and B that belong to ∂D. Since Y vanishes on Γ , it vanishes identically on any integral curve of X that contains Γ (by analyticity).

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Advances in Phase Space Analysis of Partial Differential Equations: In Honor of Ferruccio Colombini's 60th Birthday by Luigi Ambrosio (auth.), Antonio Bove, Daniele Del Santo, M.K. Venkatesha Murthy (eds.)


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