The first regularity result for elliptic equations with discontinuous coefficients was obtained by Morrey in the case of dimension 2 (The general case was proved many years later by De Giorgi and, independently by Nash). Ir remained open the problem of achieving the best possible Holder regularity according ti the information available about the ellipticity coefficient. Meyers example, with the greatest conductivity along radial paths and the least along transverse paths was very suggestive. In this paper the autors show that actually Meyers example builds the least favourable case, hence regularity Holder coefficient is exactly 1/sqr(L), thus improving all previous estimates
On the Hoelder continuity of solutions of Second Order elliptic Equations in two variables
PICCININI, Livio Clemente;
1972-01-01
Abstract
The first regularity result for elliptic equations with discontinuous coefficients was obtained by Morrey in the case of dimension 2 (The general case was proved many years later by De Giorgi and, independently by Nash). Ir remained open the problem of achieving the best possible Holder regularity according ti the information available about the ellipticity coefficient. Meyers example, with the greatest conductivity along radial paths and the least along transverse paths was very suggestive. In this paper the autors show that actually Meyers example builds the least favourable case, hence regularity Holder coefficient is exactly 1/sqr(L), thus improving all previous estimatesI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
