Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems

Arina A. Arkhipova

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2003)

  • Volume: 14, Issue: 2, page 91-108
  • ISSN: 1120-6330

Abstract

top
It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.

How to cite

top

Arkhipova, Arina A.. "Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.2 (2003): 91-108. <http://eudml.org/doc/252282>.

@article{Arkhipova2003,
abstract = {It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.},
author = {Arkhipova, Arina A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Boundary value problem; Reverse Hölder inequalities; Elliptic system; boundary value problem; reverse Hölder inequalities; elliptic system},
language = {eng},
month = {6},
number = {2},
pages = {91-108},
publisher = {Accademia Nazionale dei Lincei},
title = {Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems},
url = {http://eudml.org/doc/252282},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Arkhipova, Arina A.
TI - Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/6//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 2
SP - 91
EP - 108
AB - It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.
LA - eng
KW - Boundary value problem; Reverse Hölder inequalities; Elliptic system; boundary value problem; reverse Hölder inequalities; elliptic system
UR - http://eudml.org/doc/252282
ER -

References

top
  1. GEHRING, F.W., The L p -integrability of the partial derivatives of a quasi conformal mapping. Acta Math., 130, 1973, 265-277. Zbl0258.30021MR402038
  2. GIAQUINTA, M. - MODICA, G., Regularity results for some classes of higher order non-linear elliptic systems. J. für Reine u. Angew. Math., 311/312, 1979, 145-169. Zbl0409.35015MR549962
  3. STREDULINSKY, E.W., Higher integrability from reverce Hölder inequalities. Indiana Univ. Math. J., 29, 3, 1980, 408-417. Zbl0442.35064MR570689DOI10.1512/iumj.1980.29.29029
  4. ARKHIPOVA, A.A., Reverse Hölder inequalities with boundary integrals and L p -estimates for solution of nonlinear elliptic and parabolic boundary-value problems. Advances in Math. Sci. Translations, Ser. 2, 164, 1995, 15-42. Zbl0838.35021MR1334137
  5. ARKHIPOVA, A.A. - LADYZHENSKAYA, O.A., On a modification of Gehring lemma. Zapiski Nauchn, Semin. POMI, St-Petersburg, 259, 1999, 7-18. Zbl0979.35062
  6. ARKHIPOVA, A.A., On the regularity of the solution of the Neumann problem for quasilinear parabolic systems. Russian Acad. Sci. Izv. Math., 45, 1995, 231-253. Zbl0857.35054MR1307308DOI10.1070/IM1995v045n02ABEH001576
  7. GIAQUINTA, M., Multiple integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Annals of Math., Studies105, Princeton Univ. Press, Princeton1983. Zbl0516.49003MR717034
  8. GIAQUINTA, M. - GIUSTI, E., Non linear elliptic systems with Quadratic growth. Manuscripta Math., 24, 1978, 323-349. Zbl0378.35027MR481490
  9. KUFNER, A. - JOHN, O. - FUČIK, S., Functional Spases. Academia, Prague1977. 
  10. FREHSE, J., On two-dimensional quasi-linear elliptic systems. Manuscripta Math., 28, 1979, 21-50. Zbl0415.35025MR535693DOI10.1007/BF01647963
  11. HAMBURGER, C., A new partial regularity proof for solutions of nonlinear elliptic systems. Manuscripta Math., 95, n. 1, 1998, 11-31. Zbl0901.35013MR1492366DOI10.1007/BF02678012
  12. TROIANIELLO, G.M., Elliptic differential equations and obstacle problems. Plenum, New York-London1987. Zbl0655.35002MR1094820

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.