Soit Ω un domaine borne dans R n avec n≥3 On etudie l'existence d'une fonction u satisfaisant l'equation elliptique non lineaire -Δu=u P +f(x,u) sur Ω, u>0 sur Ω, u=0 sur ∂Ω, ou p=(n+2)/(n−2), f(x,0)=0 et f(x,u) est une perturbation de u P de bas ordre au sens ou lim u→+α f(x,u)/u P =0

Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

We evaluated the accuracy of a noninvasive method for estimating right ventricular systolic pressures in patients with tricuspid regurgitation detected by Doppler ultrasound. Of 62 patients with clinical signs of elevated right-sided pressures, 54 (87%) had jets of tricuspid regurgitation clearly recorded by continuous-wave Doppler ultrasound. By use of the maximum velocity (V) of the regurgitant jet, the systolic pressure gradient (delta P) between right ventricle and right atrium was calculated by the modified Bernoulli equation (delta P = 4V2). Adding the transtricuspid gradient to the mean right atrial pressure (estimated clinically from the jugular veins) gave predictions of right ventricular systolic pressure that correlated well with catheterization values (r = .93, SEE = 8 mm Hg). The tricuspid gradient method provides an accurate and widely applicable method for noninvasive estimation of elevated right ventricular systolic pressures.

Noninvasive estimation of right ventricular systolic pressure by Doppler ultrasound in patients with tricuspid regurgitation

Curvatures of left invariant metrics on lie groups

What Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.- Riemannian Submanifolds.- The Gauss-Bonnet Theorem.- Jacobi Fields.- Curvature and Topology.

Riemannian Manifolds: An Introduction to Curvature

/pdf/the-dirichlet-problem-for-the-fractional-laplacian-1w4qdfqmwi.pdf

The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary

Curvature Functions for Compact 2-Manifolds

Remarks on some quasilinear elliptic equations

/pdf/scalar-curvature-and-conformal-deformation-of-riemannian-1hg3teek8k.pdf

Scalar curvature and conformal deformation of Riemannian structure

In previous work [11], [13] we have considered the problem of describing the set of Gaussian curvatures (if dim M = 2) and scalar curvatures (if dim M > 3) on a compact, connected, but not necessarily orientable manifold M (see also [12] for the case of open manifolds). We refer the reader to the introductions of [11] and [13] for relevant background and literature. In this paper we give a unified proof that the obvious sign condition demanded by the Gauss Bonnet Theorem, namely,

http://www.jstor.org/stable/pdfplus/1970993.pdf

Existence and Conformal Deformation of Metrics With Prescribed Gaussian and Scalar Curvatures

I. Gaussian Curvature Surfaces in $R^3$ Prescribing the curvature form on a surface Prescribing the Gaussian curvature on a surface (a) Compact surfaces (b) Noncompact surfaces II. Scalar Curvature Topological obstructions Pointwise conformal deformations and the Yamabe problem (a) $M^n$ compact (b) $M^n$ noncompact Prescribing scalar curvature Cauchy-Riemann manifold III. Ricci Curvature Local solvability of Ric$(g)=R_ij$ Local smoothness of metrics Global topological obstructions Uniqueness, nonexistence Einstein metrics on 3-manifolds Kaahler manifolds (a) Kahler geometry (b) Calabi's problem and Kahler-Einstein metrics (c) Another variational problem IV. Boundary Value Problems Surfaces with constant mean curvature (a) Rellich's problem Some other boundary value problems (a) Graphs with prescribed mean curvature (b) Graphs with prescribed Gauss curvature The $C^2+\alpha$ estimate at the boundary Some Open Problems.

Jerry L. Kazdan

Papers

Curvature Functions for Compact 2-Manifolds

Remarks on some quasilinear elliptic equations

Scalar curvature and conformal deformation of Riemannian structure

Existence and Conformal Deformation of Metrics With Prescribed Gaussian and Scalar Curvatures

Prescribing the Curvature of a Riemannian Manifold