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A Remark on the Sobolev Regularity of Classical Solutions of Strongly Elliptic Equations
Author(s) -
Milani Albert
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981900111
Subject(s) - mathematics , sobolev space , pure mathematics , elliptic curve , mathematical analysis
We prove that C 2,α ( Ω ) solutions of problem (1.2) below are in H m+2 (Ω) for all m ∈ ℕ, if f and the coefficients are in H m (Ω) n C 0,α ( Ω ) Previously, this result was explicitly known only if m > n /2 (or if m = 0). A similar result holds for the quasi‐linear equation (1.11) below.