Time – table for the Conference

“Non Linear Functional Analysis”

Registration 8:30 am - 9:30 am - 18 January 2012

 TIME January  18th, 2012(Wednesday) January  19th, 2012(Thursday) January  20th, 2012(Friday) 9:30 – 10:15 J. C. Nedelec J.P. Raymond S. Thangavelu 10:15 – 11:00 Ph. Destuynder P. Prasad B. Rajeev 11:00 – 11:30 Tea Tea Tea 11:30 – 12:15 D. Ciorenescu O. Pironneau T. Tamishselvi 12:15 – 1:00 L. Boccardo A.K.Pani Shivashankar 1:00 – 2:00 Lunch Lunch Lunch 2:00 – 2:45 F. Pacella Adimurthi N. Sabu 2:45– 3:30 P.N. Srikanth Ciarlet( M. Vanninathan) M. Rajesh 3:30 – 4:00 Tea Tea Tea 4:00 – 4:45 M. Esteban Felicitation (4:30 pm) and Banquet (7:00 pm) T V Anoop

“On the wave equation for a subelliptic operator”

Prof. S. Thangavelu

Dept. of Mathematics, IISc, Bangalore

Abstract: We plan to discuss $L^p$ boundedness of solutions of the wave equation associated to the Grushin operator $G = -\Delta-|x|^2\partial_t^2$ on $\R^{n+1}$. We use tools from harmonic Analysis to achieve the $L^p$ estimates.

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“Optimal Control problem in Conservation Law”

TIFR- CAM, Bangalore

Abstract: Here we give an easy algorithm to capture an optimal control governed by a conservation law with strict convex flux in one space dimension.

“A fundamental lemma of J.L. Lions and its far-reaching consequences”

Prof. Philippe G. Ciarlet

City University of Hong Kong

Abstract: A fundamental lemma of J.L Lions regarding a distribution with all its partial derivatives in H^ {-1}, states that the distribution is indeed in L^2.  Several important applications of this lemma in linear and nonlinear cases are illustrated.

“Functional inequalities and the symmetry properties of the extremal functions”

Prof. Maria Esteban

Abstract: In this talk I will present recent work, in collaboration with J. Dolbeault, M. Loss, G. Tarantello and A. Tertikas, about the symmetry properties of extremal functions for (interpolation) functional inequalities playing an important role in the study of long time behavior of evolution diffusion equations. Optimal constants are rarely known; in fact one can write them explicitely only when the extremals enjoy maximal symmetry. This is why the knowledge of the parameters' regions where symmetry is achieved is of big importance.  In the case of symmetry breaking, the underlying phenomena are analysed.

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Variational forms for the inverses of integral logarithmic operators over an interval"

Prof. Jean-Claude Nedelec

Directeur de Recherches,

Centre de Mathematiques Appliquees

Ecole Polytechnique, France

Abstract: We present explicit and exact variational formulations for the weakly singular and

hypersingular operators over an interval as well as for their corresponding inverses. We show that a symmetric and antisymmetric decomposition leads to precise coercivity results in Sobolev spaces and characterize the mismatch occurring between associated functional spaces in this limiting case. Moreover, we are able to define Calder\'on-type identities in each case.

“Symmetry results for cooperative elliptic systems”

Prof. Filomena Pacella

Sapienza Université de Roma

Abstract: We show some recent results (in collaboration with L. Damascelli) on the foliated Schwarz symmetry of solutions of cooperative elliptic systems. The nonlinear term is assumed to be convex and we consider solutions having (linearized) Morse index less or equal to the dimension of the space.

“The Partial Differential Equations of Finance”

Prof. Olivier Pironneau

University of Paris VI, France

Abstract: Pdf File

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“Kinematical Conservation Laws (KCL): A mathematical model to describe evolution of curves and surfaces”

Dept. of Mathematics,

IISc, Bangalore

Abstract: Pdf File

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“Discontinous Galerkin Methods for Elliptic Problems: Old Wine in a New Bottle”

Prof. A K Pani

Industrial Mathematics Group, Department of Mathematics, IITBombay, Powai,Mumbai-400076

Abstract: Pdf File

“Water wave Simulations created by a Submarine”

Prof. Philippe Destuynder

Applied Mathematics Department, CNAM, Paris, France.

Abstract: Pdf File

“Homogenization in perforated domains”

Prof. Doina Cioranescu

Universite de Paris VI, France.

Abstract: Pdf File

“An Existence and Symmetry result for a Two-phase Eigenvalue Minimization”

Abstract: Pdf File

“W0 1,1 Solutions in some Borderline cases of Calderon-Zymund Theory”

Prof. Lucio Boccardo

Dip. Mat. Univ. Roma

Abstract: Pdf File

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"Vibrations of thin piezoelectric shells: Two dimensional approximation"

Prof. Sabu Nicholas

IIST, Trivandrum

Abstract: We consider the eigenvalue problem for thin piezoelectric shell, of thickness $\ep$, clamped along a portion of its lateral surface under the geometrical assumption that the space of inextensional displacement is infinite dimensional. We then show that the eigensolutions converge, as the thickness goes to zero, to the eigensolutions of the two-dimensional flexural shell.

"Concentration on S1 orbits for a Class of  Semi linear  Elliptic Problems".

Prof. P. N. Srikanth

TIFR-CAM, Bengaluru