Sur la nature analytique des solutions des équations aux dérivées partielles du second ordre

  title={Sur la nature analytique des solutions des {\'e}quations aux d{\'e}riv{\'e}es partielles du second ordre},
  author={Serge Bernstein},
  journal={Mathematische Annalen},
  • S. Bernstein
  • Published 1 March 1904
  • Mathematics
  • Mathematische Annalen
Geometric properties of surfaces with the same mean curvature in R^3 and L^3
Spacelike surfaces in the Lorentz-Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It isExpand
Regularity for non-autonomous convex functionals with non-standard growth conditions
In this thesis we investigate the regularity of minimizers of non-autonomous integral functionals of the calculus of variations, with non-standard growth conditions.
A pointwise differential inequality and second-order regularity for nonlinear elliptic systems
A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity propertiesExpand
Positive maximal and minimal solutions for non-homogeneous elliptic equations depending on the gradient
Abstract We are concerned with positive maximal and minimal solutions for non-homogeneous elliptic equations of the form − div ( a ( | ∇ u | p ) | ∇ u | p − 2 ∇ u ) = f ( x , u , ∇ u )  in  Ω ,Expand
Analyticity for Solution of Integro-Differential Operators
We prove that for a certain class of kernels $K(y)$ that viscosity solutions of the integro-differential equation $$ \int_{\mathbb R^n} (u(x+y) - 2 u(x) + u(x-y)) K(y) dy = f(x,u(x)) $$ are locallyExpand
On the analyticity of solutions to non-linear elliptic partial differential systems
We give an easy proof of the fact that $C^\infty$ solutions to non-linear elliptic equations of second order $$ \phi(x, u, D u, D^2 u)=0 $$ are analytic. Following ideas of Kato, the proof uses anExpand
  • C. Mouhot
  • Mathematics
  • Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
We report on recent results and a new line of research at the crossroad of two major theories in the analysis of partial differential equations. The celebrated De Giorgi-Nash-Moser theory showsExpand
On the analyticity of solutions of partial differential equations and systems
© Société mathématique de France, 1973, tous droits réservés. L’accès aux archives de la collection « Astérisque » ( Publications/Asterisque/) implique l’accord avec lesExpand
Piecewise analytic bodies in subsonic potential flow
  • V. Elling
  • Mathematics
  • Communications in Partial Differential Equations
  • 2019
Abstract We prove that there are no non-zero uniformly subsonic potential flows around piecewise analytic bodies with three or more protruding corners, assuming the equation of state is a γ-law orExpand
The weak Harnack inequality for the Boltzmann equation without cut-off
In this paper, we obtain the weak Harnack inequality and Holder estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can beExpand


Sur quelques applications géométriques des séries de Fourier
Les series de Fourier et des developpements analogues interviennent tout naturellement dans la theorie generale des courbes et des surfaces. En effet, cette theorie, envisagee au point de vue deExpand