Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity q > 1 and with natural growth

Sofia Giuffrè; Giovanna Idone

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 2, page 519-524
  • ISSN: 0392-4041

Abstract

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In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for n = q .Moreover we show that also for 1 < q < 2 , but q close enough to 2, the solutions are global Hölder continuous for n = 2 .

How to cite

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Giuffrè, Sofia, and Idone, Giovanna. "Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth." Bollettino dell'Unione Matematica Italiana 8-B.2 (2005): 519-524. <http://eudml.org/doc/195193>.

@article{Giuffrè2005,
abstract = {In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension $n=q$ without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for $n=q$.Moreover we show that also for $1<q<2$, but $q$ close enough to 2, the solutions are global Hölder continuous for $n=2$.},
author = {Giuffrè, Sofia, Idone, Giovanna},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {519-524},
publisher = {Unione Matematica Italiana},
title = {Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth},
url = {http://eudml.org/doc/195193},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Giuffrè, Sofia
AU - Idone, Giovanna
TI - Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/6//
PB - Unione Matematica Italiana
VL - 8-B
IS - 2
SP - 519
EP - 524
AB - In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension $n=q$ without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for $n=q$.Moreover we show that also for $1<q<2$, but $q$ close enough to 2, the solutions are global Hölder continuous for $n=2$.
LA - eng
UR - http://eudml.org/doc/195193
ER -

References

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