Institute for Mathematical Physics Critical Sets of Smooth Solutions to Elliptic Equations Critical Sets of Smooth Solutions to Elliptic Equations +

  • M. Hoffmann - Ostenhof, T. Hoffmann - Ostenhof, N. Nadirashvili

Abstract

Let u 6 6 const satisfy an elliptic equation L 0 u a i;j D ij u+b j D j u = 0 with smooth coeecients in a domain in R n. It is shown that the critical set jruj ?1 f0g has locally nite n ? 2-dimensional Hausdorr measure. This implies in particular that for a solution u 6 6 0 of (L 0 + c)u = 0, with c 2 C 1 , the critical zero set u ?1 f0g \ jruj ?1 f0g has… (More)

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