THE MOSER'S ITERATIVE METHOD FOR A CLASS OF ULTRAPARABOLIC EQUATIONS
By Andrea Pascucci, Sergio Polidoro. 2004
90 citations recorded by the source corpus.
We adapt the iterative scheme by Moser, to prove that the weak solutions to an ultraparabolic equation, with measurable coefficients, are locally bounded functions. Due to the strong degeneracy of the equation, our method differs from the classical one in that it is based on some ad hoc Sobolev type inequalities for solutions.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/380405b43e56f3d01f843417ab31ef40ec7aff13
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Luis Silvestre
- C. Imbert
- Alexis Vasseur
- Juan Luis V'azquez
- Clément Mouhot
- François Golse
- Francesca Anceschi
- Sergio Polidoro
In Mathematical Physics
- C. Imbert
- Luis Silvestre
- Clément Mouhot
- Francesca Anceschi
- Alexis Vasseur
- François Golse
- Sergio Polidoro
- Pascucci Andrea
Citations in the corpus
- Pointwise estimates for a class of non-homogeneous Kolmogorov equations (2008, methodology): “As in [28], we follow the lines of the proof of Theorem 1.”
- The weak Harnack inequality for the Boltzmann equation without cut-off (2016, methodology): “Pascucci and Polidoro [55] obtained the local L8 estimate for this equation using Moser’s method.”
- A survey on the classical theory for Kolmogorov equation (2019, methodology): “The theory of Kolmogorov operators with measurable coefficients aij is developed in the following papers: • Moser iteration: a first contribution is given by Polidoro and Pascucci (see [60]) for dilation invariant Kolmogorov operators with measurable coefficients; later on, Cinti, Pascucci and Polid”
- Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, methodology): “In [53], the authors obtain an L2−L∞ estimate with completely different techniques; however they cannot reach the Hölder continuity estimate.”
- Linear and nonlinear ultraparabolic equations of Kolmogorov type arising in diffusion theory and in finance (2002, methodology): “In [38], they prove the local boundedness of the weak solutions to (5.”