Microglobal Analysis

AbstractWe study some Phragmén-Lindelöf type results, which were considered as extensions of maximal modulus theorem. We shall consider them from the viewpoint of Fourier analysis. Our analysis shows that the Phragmén-Lindelöf theorems can be regarded as the convexity of microglobal wave front sets. We prove such theorems for elliptic systems of equations with constant coefficients.

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Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients

Abstract and Applied Analysis ◽

10.1155/2014/438716 ◽

2014 ◽

Vol 2014 ◽

pp. 1-17 ◽

Cited By ~ 5

Author(s):

C. Boiti ◽

D. Jornet ◽

J. Juan-Huguet

Keyword(s):

Differential Operator ◽

Wave Front ◽

Partial Differential Operator ◽

Regularity Theorem ◽

Wave Front Set ◽

Open Set ◽

Wave Front Sets ◽

Constant Coefficients ◽

New Type ◽

Classical Distribution

We introduce the wave front setWF*P(u)with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distributionu∈𝒟′(Ω)in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor. We state a version of the microlocal regularity theorem of Hörmander for this new type of wave front set and give some examples and applications of the former result.

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Global wave-front sets of Banach, Fréchet and modulation space types, and pseudo-differential operators

Journal of Differential Equations ◽

10.1016/j.jde.2013.01.014 ◽

2013 ◽

Vol 254 (8) ◽

pp. 3228-3258 ◽

Cited By ~ 13

Author(s):

Sandro Coriasco ◽

Karoline Johansson ◽

Joachim Toft

Keyword(s):

Wave Front ◽

Differential Operators ◽

Modulation Space ◽

Pseudo Differential Operators ◽

Wave Front Sets

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The Kashiwara conjugation and wave-front sets of regular holonomic distributions on a complex manifold

Inventiones mathematicae ◽

10.1007/bf01232246 ◽

1994 ◽

Vol 117 (1) ◽

pp. 357-357

Keyword(s):

Wave Front ◽

Complex Manifold ◽

Wave Front Sets

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Quasilinear elliptic systems in divergence form associated to general nonlinearities

Advances in Nonlinear Analysis ◽

10.1515/anona-2018-0171 ◽

2018 ◽

Vol 7 (4) ◽

pp. 425-447 ◽

Cited By ~ 11

Author(s):

Lorenzo D’Ambrosio ◽

Enzo Mitidieri

Keyword(s):

Positive Solutions ◽

A Priori Estimates ◽

A Priori ◽

Elliptic Systems ◽

Divergence Form ◽

Systems Of Equations ◽

Quasilinear Elliptic Systems ◽

Open Set ◽

Priori Estimates ◽

Quasilinear Elliptic

AbstractThe paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case {\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

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