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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Subelliptic Cordes estimates

Author(s): András Domokos; Juan J. Manfredi
Journal: Proc. Amer. Math. Soc. 133 (2005), 1047-1056.
MSC (2000): Primary 35H20, 35J70
Posted: November 19, 2004
MathSciNet review: 2117205
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Abstract | References | Similar articles | Additional information

Abstract: We prove Cordes type estimates for subelliptic linear partial differential operators in non-divergence form with measurable coefficients in the Heisenberg group. As an application we establish interior horizontal $W^{2,2}$-regularity for p-harmonic functions in the Heisenberg group ${\mathbb H}^1$ for the range $\frac{\sqrt{17}-1}{2} \leq p < \frac{5+\sqrt{5}}{2}$.

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H. O. Cordes, Zero order a priori estimates for solutions of elliptic differential equations, Proceedings of Symposia in Pure Mathematics IV (1961). MR 0146511 (26:4033)

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A. Domokos, Differentiability of solutions for the non-degenerate $p$-Laplacian in the Heisenberg group, J. Differential Equations 204(2004), 439-470.

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A. Domokos and Juan J. Manfredi, $C^{1,\alpha}$-regularity for p-harmonic functions in the Heisenberg group for $p$ near $2$, to appear in The $p$-harmonic equation and recent advances in analysis, Contemporary Mathematics, editor Pietro Poggi-Corradini.

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S. Marchi, $C^{1,\alpha}$ local regularity for the solutions of the p-Laplacian on the Heisenberg group for $2\leq p \leq 1+\sqrt{5}$, Z. Anal. Anwendungen 20(2001), 617-636. See Erratum, Z. Anal. Anwendungen 22 (2003), 471-472.MR 1863937 (2002i:35037); MR 2000279 (2004g:35034)

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S. Marchi, $C^{1,\alpha}$ local regularity for the solutions of the p-Laplacian on the Heisenberg group. The case $1+ \frac{1}{\sqrt{5}} < p \leq 2$ , Comment. Math. Univ. Carolinae 44(2003), 33-56. See Erratum, to appear. MR 2045844

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Additional Information:

András Domokos
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
Address at time of publication: Department of Mathematics and Statistics, California State University Sacramento, 6000 J Street, Sacramento, California 95819
Email: domokos@csus.edu

Juan J. Manfredi
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
Email: manfredi@pitt.edu

DOI: 10.1090/S0002-9939-04-07819-0
PII: S 0002-9939(04)07819-0
Keywords: Cordes conditions, subelliptic equations, p-Laplacian
Received by editor(s): August 13, 2003
Posted: November 19, 2004
Additional Notes: The authors were partially supported by NSF award DMS-0100107
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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