Eigenvalues of the time-dependent fluid flow problem. I.
Let be an open set with a compact boundary and let be a finite measure on . Consider the space of all -integrable functions on and, for each...
The -convex functions are the viscosity subsolutions to the fully nonlinear elliptic equations , where is the elementary symmetric function of order , , of the eigenvalues of the Hessian matrix . For example, is the Laplacian and is the real Monge-Ampère operator det , while -convex functions and -convex functions are subharmonic and convex in the classical sense, respectively. In this paper, we establish an approximation theorem for negative -convex functions, and give several...
We establish inequalities for Green functions on general bounded piecewise Dini-smooth Jordan domains in ℝ². This enables us to prove a new version of the 3G Theorem which generalizes its previous version given in [M. Selmi, Potential Anal. 13 (2000)]. Using these results, we give a comparison theorem for the Green kernel of Δ and the Green kernel of Δ - μ, where μ is a nonnegative and exact Radon measure.
We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.