Students and Courses Research
My research interests is analysis and nonlinear PDEs, in particular the application of measure theoretic techniques to
hyperbolic and transport equations. To have a brief overview of my research, these are in my opinion the most important papers:
- S. Bianchini, A. Bressan, VANISHING
VISCOSITY SOLUTIONS OF NONLINEAR
Annals of Mathematics 161
(2005), pag. 223-342.
Proof of the convergence of the vanishing viscosity approximations to the hyperbolic solution for system of conservation laws.
The viscosity is the identity matrix.
- S. Bianchini, L. Caravenna,
SBV REGULARITY FOR GENUINELY NONLINEAR, STRICTLY HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN ONE SPACE DIMENSION,
Comm. Math. Phys. 313 (2012), 1-33.
Solution to the SBV regularity problem for solutions to genuinely nonlinear hyperbolic systems.
- S. Bianchini, S. Modena,
QUADRATIC INTERACTION FUNCTIONAL FOR GENERAL SYSTEMS OF CONSERVATION LAWS
, Communications in Mathematical Physics
338, p. 1075-1152.
The quadratic interaction estimate for general strictly hyperbolic systems of conservation laws in one space dimension.
- S. Bianchini, E. Marconi,
ON THE STRUCTURE OF $L^\INFTY$-ENTROPY SOLUTIONS TO SCALAR CONSERVATION LAWS IN ONE-SPACE DIMENSION
, Archive for Rational Mechanics and Analysis
226 (1), p. 441-493.
Here the structure of $L^\infty$-entropy solutions to conservation laws is described in full details, yielding in particular the proof of
the conjecture on the concentration of the entropy dissipation.
S. Bianchini, L. Caravenna, ON THE EXTREMALITY, UNIQUENESS AND
OPTIMALITY OF TRANSFERENCE PLANS, Bullettin of the Institute of
Mathematics, Academia Sinica Taipei 4 (2009), p. 353-454.
Title is self explanatory: the key argument is a uniqueness results for plans concentrated on and Borel linear preorder.
- S. Bianchini, S. Daneri,
ON SUDAKOV'S TYPE DECOMPOSITION OF TRANSFERENCE PLANS WITH NORM COSTS, Memoirs AMS 251, n. 1197.
The solution of the Monge transportation problem with convex norm using the Sudakov approach.
- G. Alberti, S. Bianchini, G. Crippa,
A UNIQUENESS RESULT FOR THE CONTINUITY EQUATION IN TWO DIMENSIONS, Journal EMS
16, p. 201-234.
Complete description of weak solutions to 2d autonomous divergence free linear transport.
- S. Bianchini, P. Bonicatto,
A UNIQUENESS RESULT FOR THE DECOMPOSITION OF VECTOR FIELDS IN R^d
, preprint SISSA 2017.
Solution to the
Bressan's compactness conjecture
Advanced Workshop on Hyperbolic Conservation Laws and
International Conference on Nonlinear Differential Equations-Theory, Modeling and Computations
SRM university, Chennai, December 4-9, 2017
Equazioni alle Derivate Parziali nella Dinamica dei Fluidi
CRM, Pisa, February 5-7, 2018
HYP2018 - XVII International Conference on Hyperbolic Problems Theory, Numerics, Applications
University Park, Pennsylvania, USA, June 25-29, 2018
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
Taipei, Taiwan, July 5-9, 2018
International Workshop on Hyperbolic and Kinetic
Problems: Theory and Applications
Taipei, Taiwan, July 10-14, 2018
Via Bonomea 265
E-mail : bianchin at sissa it
Public Key: Stefano Bianchini firstname.lastname@example.org (0xEB7F2E50) pub.asc
Last update: November 15, 2017