Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Subelliptic Cordes estimates
HTML articles powered by AMS MathViewer

by András Domokos and Juan J. Manfredi PDF
Proc. Amer. Math. Soc. 133 (2005), 1047-1056 Request permission

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 $\frac {\sqrt {17}-1}{2} \leq p < \frac {5+\sqrt {5}}{2}$.
References
  • Luca Capogna, Donatella Danielli, and Nicola Garofalo, An embedding theorem and the Harnack inequality for nonlinear subelliptic equations, Comm. Partial Differential Equations 18 (1993), no. 9-10, 1765–1794. MR 1239930, DOI 10.1080/03605309308820992
  • H. O. Cordes, Zero order a priori estimates for solutions of elliptic differential equations, Proc. Sympos. Pure Math., Vol. IV, American Mathematical Society, Providence, R.I., 1961, pp. 157–166. MR 0146511
  • A. Domokos, Differentiability of solutions for the non-degenerate $p$-Laplacian in the Heisenberg group, J. Differential Equations 204(2004), 439-470.
  • 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.
  • David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0
  • Guozhen Lu, Polynomials, higher order Sobolev extension theorems and interpolation inequalities on weighted Folland-Stein spaces on stratified groups, Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 3, 405–444. MR 1787096, DOI 10.1007/PL00011552
  • S. Marchi, $C^{1,\alpha }$ local regularity for the solutions of the $p$-Laplacian on the Heisenberg group for $2\leq p<1+\sqrt 5$, Z. Anal. Anwendungen 20 (2001), no. 3, 617–636. MR 1863937, DOI 10.4171/ZAA/1035
  • Silvana 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. Carolin. 44 (2003), no. 1, 33–56. MR 2045844
  • Duy-Minh Nhieu, Extension of Sobolev spaces on the Heisenberg group, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 12, 1559–1564 (English, with English and French summaries). MR 1367807
  • Robert S. Strichartz, $L^p$ harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Anal. 96 (1991), no. 2, 350–406. MR 1101262, DOI 10.1016/0022-1236(91)90066-E
  • Giorgio Talenti, Sopra una classe di equazioni ellittiche a coefficienti misurabili, Ann. Mat. Pura Appl. (4) 69 (1965), 285–304 (Italian). MR 201816, DOI 10.1007/BF02414375
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35H20, 35J70
  • Retrieve articles in all journals with MSC (2000): 35H20, 35J70
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
  • MR Author ID: 205679
  • Email: manfredi@pitt.edu
  • Received by editor(s): August 13, 2003
  • Published electronically: November 19, 2004
  • Additional Notes: The authors were partially supported by NSF award DMS-0100107
  • Communicated by: David S. Tartakoff
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1047-1056
  • MSC (2000): Primary 35H20, 35J70
  • DOI: https://doi.org/10.1090/S0002-9939-04-07819-0
  • MathSciNet review: 2117205