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

Bollettino dell'Unione Matematica Italiana (2005)

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

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topGiuffrè, 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 -

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