J
Jean Dolbeault
Researcher at Paris Dauphine University
Publications - 308
Citations - 7911
Jean Dolbeault is an academic researcher from Paris Dauphine University. The author has contributed to research in topics: Sobolev inequality & Nonlinear system. The author has an hindex of 42, co-authored 293 publications receiving 7072 citations. Previous affiliations of Jean Dolbeault include Paul Sabatier University & PSL Research University.
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Convex Sobolev inequalities and spectral gap
TL;DR: In this article, it was shown that spectral gap inequalities imply all convex Sobolev inequalities with constants which are uniformly bounded in the limit approaching the logarithmic Sobolerv inequalities.
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Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case
Jean Dolbeault,Patricio Felmer +1 more
TL;DR: In this article, the authors prove local monotonicity and symmetry properties for nonnegative solutions of scalar field equations with nonlinearities which are not Lipschitz, using a local moving plane method and a unique continuation argument.
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From Poincar\'e to logarithmic Sobolev inequalities: a gradient flow approach
TL;DR: In this paper, a unified framework for the study of the Kolmogorov-Fokker-Planck (KFP) equation is presented. But the framework is not suitable for the analysis of drift-diffusion equations.
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General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators.
TL;DR: In this article, an extension and reinterpretation of previous results on variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators is presented.
Nonlinear diusions, hypercontractivity and the optimal L p -Euclidean logarithmic Sobolev inequality
TL;DR: In this article, the existence and uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the L p -Euclidean logarithmic Sobolev inequality were investigated.