A5064499639- Advanced Harmonic Analysis Research
- Nonlinear Partial Differential Equations
- Advanced Mathematical Modeling in Engineering
- Advanced Mathematical Physics Problems
- Mathematical Analysis and Transform Methods
- Differential Equations and Boundary Problems
- Spectral Theory in Mathematical Physics
- Numerical methods in inverse problems
- Holomorphic and Operator Theory
- Stability and Controllability of Differential Equations
- Advanced Banach Space Theory
- Navier-Stokes equation solutions
- Mathematical Approximation and Integration
- Geometric Analysis and Curvature Flows
- Image and Signal Denoising Methods
- Advanced Numerical Analysis Techniques
- advanced mathematical theories
- Matrix Theory and Algorithms
- Stochastic processes and financial applications
- Geometry and complex manifolds
- Algebraic and Geometric Analysis
- Mathematical functions and polynomials
- Numerical methods in engineering
- Digital Filter Design and Implementation
- Numerical methods for differential equations
Centre National de la Recherche Scientifique
2011-2024
Université Paris-Saclay
2016-2024
Laboratoire de Mathématiques d'Orsay
2015-2024
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
1999-2022
Université de Picardie Jules Verne
1999-2021
Université Paris-Sud
2010-2019
Université Paris Cité
1992-2018
Australian National University
2011-2017
Laboratoire de Mathématiques
2003-2014
Brown University
1995-1998
We prove the Kato conjecture for elliptic operators on Jfin. More precisely, we establish that domain of square root a uniformly complex operator L =-div (AV) with bounded measurable coefficients in IEtn iS
One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. shows that Riesz transform is Lp bounded on such a manifold, for p ranging in an open interval 2, if only gradient certain estimate same p's. On considère la classe des variétés riemanniennes complètes non compactes dont le noyau de chaleur satisfait une estimation supérieure et inférieure gaussienne. montre que transformée y est bornée sur Lp, pour un...
We consider second order elliptic divergence form systems with complex measurable coefficients A that are independent of the transversal coordinate, and prove set for which boundary value problem L2 Dirichlet or Neumann data is well posed, an open set. Furthermore we these problems posed when either Hermitean, block constant. Our methods apply to more general partial differential equations as example perturbation results forms.
Given any elliptic system with t -independent coefficients in the upper-half space, we obtain representation and trace for conormal gradient of solutions natural classes boundary value problems Dirichlet Neumann types area integral control or non-tangential maximal control. The spaces are obtained a range which is parametrized by properties some Hardy spaces. This implies complete picture uniqueness vs solvability well-posedness.
We give a new proof of Aronson's upper gaussian bound on the heat kernel for parabolic equations with time-independent real measurable coefficients. This approach also gives bounds in case complex perturbation coefficients and uniformly continuous complex-valued
We show various L p estimates for Schrödinger operators -Δ+V on ℝ n and their square roots. assume reverse Hölder the potential, improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities weak solutions gradients.
We develop some connections between interpolation theory and the of bounded holomorphic functional calculi operators in Hilbert spaces, via quadratic estimates. In particular we show that an operator T type ! has a calculus if only space is complex midway completion its domain range. also characterise spaces domains all fractional powers , whether or not calculus. This treatment extends earlier ones for self{adjoint maximal accretive operators. work motivated by study rst order elliptic...