# Functional Inequalities: Nonlinear Flows and Entropy Methods as a Tool for Obtaining Sharp and Constructive Results

@article{Dolbeault2021FunctionalIN, title={Functional Inequalities: Nonlinear Flows and Entropy Methods as a Tool for Obtaining Sharp and Constructive Results}, author={Jean Dolbeault}, journal={Milan Journal of Mathematics}, year={2021} }

Interpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various other areas of Science. Research interests have evolved over the years: while mathematicians were originally focussed on abstract properties (for instance appropriate notions of functional spaces for the existence of weak solutions in PDEs), more qualitative…

## 2 Citations

Intermittent symmetry breaking and stability of the sharp Agmon--H\"ormander estimate on the sphere

- Mathematics
- 2021

We compute the optimal constant and characterise the maximisers at all spatial scales for the Agmon–Hörmander L-Fourier adjoint restriction estimate on the sphere. The maximisers switch back and…

Functional inequalities and applications to doubly nonlinear diffusion equations

- Mathematics
- 2021

We study weighted inequalities of Hardy and Hardy–Poincaré type and find necessary and sufficient conditions on the weights so that the considered inequalities hold. Examples with the optimal…

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