✦ LIBER ✦

A quantitative form of the maximum priniciple for elliptic partial differential equations with coefficients in L∞

✍ Scribed by Kjell-Ove Widman

Publisher: John Wiley and Sons
Year: 1968
Tongue: English
Weight: 238 KB
Volume: 21
Category: Article
ISSN: 0010-3640
DOI: 10.1002/cpa.3160210505

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✦ Synopsis

KJELL-OVE WIDMAN

We shall consider (weak) solutions of the equation in a bounded domain R c R", n 5 2. The equation is supposed to satisfy aaj E L , , A, IEi2 5 ai*[Jj 5 AZ IEI2, a*j = aji. If R satisfies an internal sphere condition, we can prove THEOREM 1 . Let u be a bounded solution of (1) in R, and let X , be any point in Q.

Then to every y > 0 there exist constants K , = K,(Q, L, X , , u(X,)m) and K , = K,(Q, L, X , , Mu(X,)), where m = infn u, M = supn u, such that (2) u ( X ) -M I --Kz Sn"+"(X),

📜 SIMILAR VOLUMES

A Cauchy integral formula for a class of

A Cauchy integral formula for a class of elliptic systems of partial differential equations of first order in the space

✍ Bernd Goldschmidt 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 451 KB 👁 1 views

## Abstract This paper is a continuation of [6]. Here we construct a CAUCHY integral formula and a POMPEJU‐representation for elliptic systems of partial differential equations of first order in __R^n^__, which may be described with the help of a CLIFFORD‐algebra. Moreover we study properties of th