Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 33, 2008, 143-158

ON PLANAR BELTRAMI EQUATIONS AND HÖLDER REGULARITY

Tonia Ricciardi

Università di Napoli Federico II, Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Via Cintia, 80126 Napoli, Italy; tonia.ricciardi 'at' unina.it

Abstract. We provide estimates for the Hölder exponent of solutions to the Beltrami equation \bard f = \mu d f + \nu\overline{d f}, where the Beltrami coefficients \mu,\nu satisfy |||\mu| + |\nu|||_\infty < 1 and Im(\nu) = 0. Our estimates depend on the arguments of the Beltrami coefficients as well as on their moduli. Furthermore, we exhibit a class of mappings of the "angular stretching" type, on which our estimates are actually attained.

2000 Mathematics Subject Classification: Primary 30C62; Secondary 35J25.

Key words: Linear Beltrami equation, Hölder regularity, angular stretching.

Reference to this article: T. Ricciardi: On planar Beltrami equations and Hölder regularity. Ann. Acad. Sci. Fenn. Math. 33 (2008), 143-158.

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