[Dottorcomp] Fwd: RISM course

[Pierluigi Colli]

Giro questa informazione ai dottorandi,
PC

---------- Forwarded message ---------
Da: Cassani Daniele <daniele.cassani a uninsubria.it>
Date: mar 15 set 2020 alle ore 08:20
Subject: RISM course

Dear Coordinators of PhD schools in partnership with RISM,

the conference activity of RISM will resume in the hybrid form which will
involve a limited number of selected *participants in presence and
*participants
who will have *virtual seats *in the conference room at villa Toeplitz. The
first appointment in this new format will be the *RISM course by **Italo
Capuzzo Dolcetta* which has been postponed because of the lockdown. The
fourth edition of this intensive PhD lectures will be on *Maximum Principle and
Detours* (please find content below) and it has been rescheduled in the
week *November 16th-20th, 2020*.

Lectures will start at 10.30 from Monday to Friday.

The course is offered to all interested PhD students and postdocs. After
lectures, in the afternoon session, participants, in presence and virtual,
will have a stimulating, safe and comfortable environment to study and
share their research.

Interested people have to apply by specifying if interested to participate
in *presence *or from *remote *by sending an email with CV to

presidente a rism.it

*IMPORTANT:* Participants in presence will have lodging and local expenses
covered by RISM and among them, a few selected participants will be the
recipient of *500,00 Euro* *RISM scholarship.*

Please forward this announcement to anybody you think might be interested.

Please find further details and updates at the link www.rism.it


Best regards,

Daniele Cassani


*Maximum Principle and Detours (by Italo Capuzzo Dolcetta), November 16th -
20th, 2020 at RISM - Villa Toeplitz, Varese*

The topic of this RISM course will be the validity, at different levels of
generality, of the maximum Principle for elliptic degenerate operators and
possible applications. The course will include the following main topics:

   1. Elementary cases: linear, convex and harmonic functions.
   2. Maximum Principle for uniformly elliptic operators on bounded
   domains. The theorem Alexandrov-Bakelman-Pucci (ABP). Applications and a
   priori estimates.
   3. Generalized subharmonic functions, super-solutions in the sense of
   Calabi, viscosity supersolutions. Nonlinear version of the ABP theorem.
   4. Maximum Principle for fully nonlinear operators on bounded domains.
   5. Discrete Perron-Frobenius’ theory. Collatz-Wielandt representation
   formulas. On the validity of the Maximum Principle and positivity of  the
   principal eigenvalue.

   *Bibliography:*

   [1] M. Protter and H. Weinberger, *Maximum Principles in Differential
   Equations*, Prentice-Hall, 1967

   [2] D. Gilbarg and N. Trudinger, *Elliptic Partial Differential
   Equations of Second Order*, Springer, 1983

   [3] L. Hormander, *Notions of Convexity, *Modern Birkhauser Classics,
   Birkhauser Basel, 1994

   [4] L. Caffarelli and X. Cabré, *Fully Nonlinear Elliptic
Equations,* Colloquium
   Publications, Vo. 43, AMS 1995

   [5] M. G. Crandall, H. Ishii and P. L. Lions, *User's Guide to Viscosity
   Solutions of Second Order Partial Differential Equations*, Bulletin Ams,
   Vol. 27, No. 1, 1992

   [6] M. Bardi, I. Capuzzo Dolcetta, *Optimal Control and Viscosity
   Solutions of Hamilton-Jacobi-Bellman Equations*, Modern Birkhauser
   Classics, Birkhauser Basel, 2008

   [7]  H. Berestycki, L. Nirenberg, and S.R.S. Varadhan, *The principal
   eigenvalue and maximum principle for second-order elliptic operators in
   general domains*. Comm. Pure Appl. Math. 47 (1994), no. 1

   [8] I. Capuzzo-Dolcetta, F. Leoni, A. Vitolo, *The
   Alexandrov-Bakelman-Pucci weak maximum principle for fully nonlinear
   equations in unbounded domains*, Communications in Partial Differential
   Equations 30 (12), 1863-1881, 2005

   [9] I. Capuzzo Dolcetta, A. Vitolo, *Directional ellipticity on special
   domains: weak Maximum and Phragmen-Lindel of principles,  Nonlinear
   Analysis 184, 69-82, 2019*

   [10] H. Berestycki, I. Capuzzo Dolcetta, A. Porretta, L. Rossi,
*Maximum Principle and
   generalized principal eigenvalue for degenerate elliptic operators*, Journal
   de Mathématiques Pures et Appliquées 103 (5), 1276-1293, 2015




__
Prof. Dr. Daniele Cassani
Dip. di Scienza e Alta Tecnologia
Università degli Studi dell’Insubria
President of RISM - Riemann International School of Mathematics
Villa Toeplitz, Via G.B. Vico, 46
21100 Varese - Italy
Tel.: +39 0332 21 8771
Cell.: +39 333 3839224
www.rism.it
www.uninsubria.it/hpp/daniele.cassani
<https://www.uninsubria.it/hpp/daniele.cassani>
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