Exterior Monge–Ampère solutions

Exterior Monge-Ampère Solutions

We discuss the Siciak-Zaharjuta extremal function of a real convex body in Cn, a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphic ...

Exterior Monge- Amp`ere Solutions

We discuss the Siciak-Zaharjuta extremal function of a real convex body in C n , a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphi...

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Exterior ows at low Reynolds numbers: concepts, solutions, and applications

We discuss ‡uid structure interaction for exterior ‡ows, for Reynolds numbers ranging from about one to several thousand. New applications demand a better quantitative understanding of the details of such ‡ows, and this has stimulated a revival of interest in this topic. Astonishingly, in spite of the apparent simplicity of low Reynolds number ‡ows, their precise prediction turns out to be nume...

POSITIVE SOLUTIONS OF INEQUALITY WITH p-LAPLACIAN IN EXTERIOR DOMAINS

In the paper the differential inequality ∆pu +B(x, u) 6 0, where ∆pu = div(‖∇u‖ ∇u), p > 1, B(x, u) ∈ C( n × , ) is studied. Sufficient conditions on the function B(x, u) are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.