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Second Order Nonlinear Evolution Inclusions Existence and Relaxation Results

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Acta Mathematica Sinica,English Series 2005年第5期21卷 977-996页

作者： NikolaosS.PAPAGEORGIOU NikolaosYANNAKAKIS Department of Mathematics National Technical UniversityZografou CampusAthens 15780Greece

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.

关键词： Evolution triple Pseudomonotone and demicontinuous operator Coercive operator L-pseudomonotonicity Upper semicontinuous and lower semicontinuous multifunction Solution set Integration by parts formula compact embedding Extremal solutions Strong relaxation Hyperbolic control system Surjective operator

On Supercontractivity for Markov Semigroups

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Acta Mathematica Sinica,English Series 2007年第5期23卷 905-914页

作者： Yong Hua MAO School of Mathematical Science Beijing Normal University Beijing 100875 P. R. China

In this paper, we study the supercontractivity for Maxkov semigroups and obtain some sufficient and necessary conditions; especially explicit formulae are obtained for birth-death process and diffusion on the line. Sufficient conditions and necessary conditions in terms of isoperimetric inequalities are also presented. Moreover, we prove that the supercontractivity is equivalent to the compact embedding of Sobolev space into an Orlicz space.

关键词： Markov semigroup logarithmic Sobolev inequality supercontractivity compact embedding

L^P-Poincaré Inequality for General Symmetric Forms

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Acta Mathematica Sinica,English Series 2009年第12期25卷 2055-2064页

作者： Yong Hua MAO School of Mathematical Science LMCS Ministing of Education Beijing Normal University Beijing 100875 P. R. China

Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.

关键词： Lp Poincare inequality symmetric form isoperimetric constant compact embedding concentration

On the Empty Essential Spectrum for Markov Processes in Dimension One

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Acta Mathematica Sinica,English Series 2006年第3期22卷 807-812页

作者： Yong Hua MAO Department of Mathematics Beijing Normal University

This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general M... 详细信息

关键词： Markov generator Essential spectrum compact embedding Hardy-type inequality