Proceedings of the American Mathematical Society

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
Retrieve article in: PDF DVI PostScript

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 $\frac{\sqrt{17}-1}{2} \leq p < \frac{5+\sqrt{5}}{2}$ .

1.: L. Capogna, D. Danielli and N. Garofalo, An embedding theorem and the Harnack inequality for nonlinear subelliptic equations, Comm. Partial Differential Equations, 18(1993), 1765-1794. MR 1239930 (94j:35038)
2.: 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)
3.: A. Domokos, Differentiability of solutions for the non-degenerate -Laplacian in the Heisenberg group, J. Differential Equations 204(2004), 439-470.
4.: A. Domokos and Juan J. Manfredi, $C^{1,\alpha}$ -regularity for p-harmonic functions in the Heisenberg group for near , to appear in The -harmonic equation and recent advances in analysis, Contemporary Mathematics, editor Pietro Poggi-Corradini.
5.: D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. MR 0737190 (86c:35035)
6.: G. Lu, Polynomials, higher order Sobolev extension theorems and interpolation inequalities on weighted Folland-Stein spaces on stratified groups, Acta Math. Sinica, English Series, 16(2000), 405-444.MR 1787096 (2001k:46054)
7.: 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)
8.: 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
9.: D. Nhieu, Extension of Sobolev spaces on the Heisenberg group, C. R. Acad. Sci. Ser. I Math., 321(1995), 1559-1564.MR 1367807 (98c:22011)
10.: R. S. Strichartz, Harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Analysis, 96(1991), 350-406.MR 1101262 (92d:22015)
11.: G. Talenti, Sopra una classe di equazioni ellitiche a coeficienti misurabili, Ann. Mat. Pura. Appl. 69(1965), 285 - 304.MR 0201816 (34:1698)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35H20, 35J70

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.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS