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Currently displaying 1 – 2 of 2

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On the Newton partially flat minimal resistance body type problems

M. Comte; Jesus Ildefonso Díaz — 2005

Journal of the European Mathematical Society

We study the flat region of stationary points of the functional $\int_{Ω} F (| \nabla u (x) |) d x$ under the constraint $u \leq M$ , where $Ω$ is a bounded domain in $ℝ^{2}$ . Here $F (s)$ is a function which is concave for $s$ small and convex for $s$ large, and $M > 0$ is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when $Ω$ is a ball. We also analyze some other qualitative properties. Moreover, we show the...

A nonexistence result for a nonlinear equation involving critical Sobolev exponent

A. Carpio Rodriguez; M. Comte; R. Lewandowski — 1992

Annales de l'I.H.P. Analyse non linéaire

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