5 citations · 6 across the 6 of their papers we have counts for
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Convex Sobolev inequalities and spectral gap
Jean Dolbeault, Jean-Philippe Bartier
This note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev…
On the one-dimensional parabolic obstacle problem with variable coefficients
Adrien Blanchet, Jean Dolbeault, Regis Monneau
This note is devoted to continuity results of the time derivative of the solution to the one-dimensional parabolic obstacle problem with variable coefficients. It applies to the sm…
A nonlinear fourth-order parabolic equation and related logarithmic Sobolev inequalities
J. Dolbeault, I. Gentil, A. Jungel
A nonlinear fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary…
Oscillating minimizers of a fourth order problem invariant under scaling
R. Benguria, I. Catto, J. Dolbeault +1
By variational methods, we prove the inequality: $$ \int_{\mathbb{R}} u''{}^2 dx-\int_{\mathbb{R}} u'' u^2 dx\geq I \int_{\mathbb{R}} u^4 dx\quad \forall u\in L^4({\mathbb{R}}) {su…