Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 1093-1099

REGULARITY OF THE DERIVATIVES OF p-ORTHOTROPIC FUNCTIONS IN THE PLANE FOR 1 < p < 2

Diego Ricciotti

University of South Florida, Department of Mathematics and Statistics
4202 East Fowler Avenue, Tampa, FL 33620, U.S.A.; ricciotti 'at' usf.edu

Abstract. We present a proof of the C¹ regularity of p-orthotropic functions in the plane for 1 < p < 2, based on the monotonicity of the derivatives. Moreover we achieve an explicit logarithmic modulus of continuity.

2010 Mathematics Subject Classification: Primary 35J70, 35B65.

Key words: Singular problems, degenerate elliptic equations, regularity.

Reference to this article: D. Ricciotti: Regularity of the derivatives of p-orthotropic functions in the plane for 1 < p < 2. Ann. Acad. Sci. Fenn. Math. 44 (2019), 1093-1099.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4456