Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach

B. Franchi; R. Serapioni

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

  • Volume: 14, Issue: 4, page 527-568
  • ISSN: 0391-173X

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Franchi, B., and Serapioni, R.. "Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 14.4 (1987): 527-568. <http://eudml.org/doc/84017>.

@article{Franchi1987,
author = {Franchi, B., Serapioni, R.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Harnack inequality; Hölder continuity; Moser technique; weighted Sobolev embedding},
language = {eng},
number = {4},
pages = {527-568},
publisher = {Scuola normale superiore},
title = {Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach},
url = {http://eudml.org/doc/84017},
volume = {14},
year = {1987},
}

TY - JOUR
AU - Franchi, B.
AU - Serapioni, R.
TI - Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 4
SP - 527
EP - 568
LA - eng
KW - Harnack inequality; Hölder continuity; Moser technique; weighted Sobolev embedding
UR - http://eudml.org/doc/84017
ER -

References

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  5. [Ch.W.] S. Chanillo - R.L. Wheeden, "Harnack's Inequality and Mean Value Inequalities for Solutions of Degenerate Elliptic Equations". Comm. in Partial Differential Equations11 (1986), 1111-1134. Zbl0634.35035MR847996
  6. [D.T.] E. Di Benedetto - N. Trudinger, "Harnack Inequalities for quasi minima of variational integrals" Annales de l'Institute Henri Poincaré. Analyse non lineare1 (1984), 295-308. Zbl0565.35012MR778976
  7. [F.L.1] B. Franchi - E. Lanconelli, "Une metrique associee a una classe d'operateurs elliptiques degeneres "; Proceedings of the meeting-Linear Partial and Pseudo differential Operators. Rend. Sem. Mat. Univ. e Politec. Torino (1982). Zbl0553.35033
  8. [F.L.2] B. Franchi - E. Lanconelii, "Holder regularity theorem for a class of linear non uniformly elliptic operators with measurable coefficients". Ann. Scuola Norm. Sup. Pisa4 (1983), 523-541. Zbl0552.35032MR753153
  9. [F.L.3] B. Franchi - E. Lanconelli, "An embedding theorem for Sobolev spaces related to non smooth vector fields and Harnack inequality". Comm. in Partial Differential Equations9 (1984), 1237-1264. Zbl0589.46023MR764663
  10. [F.K.S] E. Fabes - C. Kenig - R. Serapioni, "The local regularity of solutions of degenerate elliptic equations". Comm. in Partial Differential Equations7 (1982), 77-116. Zbl0498.35042MR643158
  11. [F.P.] C. Fefferman - D. Phong, "Subelliptic eigenvalue problems". Conference on Harmonic Analysis (Chicago1981) W. Beckner et al. ed., Wadsworth (1981), 590-606. Zbl0503.35071MR730094
  12. [J.] D. Jerison, "The Poincaré inequality for vector fields satisfying Hormander's condition". Duke Math. J.53 (1986), 503-524. Zbl0614.35066MR850547
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  14. [N.S.W.] A. Nagel - E.M. Stein - S. Wainger, "Balls and metrics defined by vector fields I: Basic properties". Acta Mathematica, 155 (1985), 103-147. Zbl0578.32044MR793239
  15. [Sc] V. Scornazzani, "Pointwise Estimates for Minimizers of Some Non-Uniformly Degenerate Functionals". To appear. Zbl0699.49011
  16. [Sta] G. Stampacchia, "Le probleme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus". Ann. Inst. Fourier Grenoble15 (1965), 189-258.. Zbl0151.15401MR192177
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Citations in EuDML Documents

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  1. Francesca Lascialfari, David Pardo, Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator
  2. Maria Manfredini, Compact embedding theorems for generalized Sobolev spaces
  3. Albo Carlos Cavalheiro, The Neumann problem for some degenerate elliptic equations
  4. Albo Carlos Cavalheiro, Regularity of weak solutions to certain degenerate elliptic equations
  5. Vittorio Scornazzani, Pointwise estimates for minimizers of some non-uniformly degenerate functionals
  6. Bruno Franchi, Guozhen Lu, Richard L. Wheeden, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
  7. Bruno Franchi, Cristian E. Gutiérrez, Richard L. Wheeden, Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators
  8. Wheeden, Richard L., Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient
  9. Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Trace inequalities for Carnot-Carathéodory spaces and applications

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