On the best Hölder exponent for two dimensional elliptic equations in divergence form

Author:
Tonia Ricciardi

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2771-2783

MSC (2000):
Primary 35J15

Published electronically:
April 14, 2008

MathSciNet review:
2399041

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain an estimate for the Hölder continuity exponent for weak solutions to the following elliptic equation in divergence form:

**1.**Ennio De Giorgi,*Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari*, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3)**3**(1957), 25–43 (Italian). MR**0093649****2.**Raffaella Giova,*A weighted Wirtinger inequality*, Ricerche Mat.**54**(2005), no. 1, 293–302 (2006). MR**2290221****3.**Tadeusz Iwaniec and Carlo Sbordone,*Quasiharmonic fields*, Ann. Inst. H. Poincaré Anal. Non Linéaire**18**(2001), no. 5, 519–572 (English, with English and French summaries). MR**1849688**, 10.1016/S0294-1449(00)00058-5**4.**Charles B. Morrey Jr.,*On the solutions of quasi-linear elliptic partial differential equations*, Trans. Amer. Math. Soc.**43**(1938), no. 1, 126–166. MR**1501936**, 10.1090/S0002-9947-1938-1501936-8**5.**Jürgen Moser,*A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations*, Comm. Pure Appl. Math.**13**(1960), 457–468. MR**0170091****6.**J. Nash,*Continuity of solutions of parabolic and elliptic equations*, Amer. J. Math.**80**(1958), 931–954. MR**0100158****7.**L. C. Piccinini and S. Spagnolo,*On the Hölder continuity of solutions of second order elliptic equations in two variables*, Ann. Scuola Norm. Sup. Pisa (3)**26**(1972), 391–402. MR**0361422****8.**Tonia Ricciardi,*A sharp Hölder estimate for elliptic equations in two variables*, Proc. Roy. Soc. Edinburgh Sect. A**135**(2005), no. 1, 165–173. MR**2119847**, 10.1017/S0308210500003826**9.**Tonia Ricciardi,*A sharp weighted Wirtinger inequality*, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8)**8**(2005), no. 1, 259–267 (English, with English and Italian summaries). MR**2122985**

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Additional Information

**Tonia Ricciardi**

Affiliation:
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy

Email:
tonia.ricciardi@unina.it

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-08809-6

Keywords:
Linear elliptic equation,
measurable coefficients,
H\"older regularity

Received by editor(s):
November 25, 2005

Received by editor(s) in revised form:
March 9, 2006

Published electronically:
April 14, 2008

Additional Notes:
The author was supported in part by the INdAM-GNAMPA Project Funzionali policonvessi e mappe quasiregolari and by the MIUR National Project Variational Methods and Nonlinear Differential Equations.

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2008
American Mathematical Society