On some L p -estimates for solutions of elliptic equations in unbounded domains

Sara Monsurrò; Maria Transirico

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 4, page 507-515
  • ISSN: 0862-7959

Abstract

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In this review article we present an overview on some a priori estimates in L p , p > 1 , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two L p -bounds, p > 2 , for the solution of the associated Dirichlet problem, obtained in correspondence with two different sign assumptions. Then, putting together the above mentioned bounds and using a duality argument, we extend the estimate also to the case 1 < p < 2 , for each sign assumption, and for a data in L p ∩ L 2 .

How to cite

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Monsurrò, Sara, and Transirico, Maria. "On some $L^{p}$-estimates for solutions of elliptic equations in unbounded domains." Mathematica Bohemica 140.4 (2015): 507-515. <http://eudml.org/doc/271827>.

@article{Monsurrò2015,
abstract = {In this review article we present an overview on some a priori estimates in $L^p$, $p>1$, recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two $L^p$-bounds, $p>2$, for the solution of the associated Dirichlet problem, obtained in correspondence with two different sign assumptions. Then, putting together the above mentioned bounds and using a duality argument, we extend the estimate also to the case $1<p<2$, for each sign assumption, and for a data in $L^p\cap L^2$.},
author = {Monsurrò, Sara, Transirico, Maria},
journal = {Mathematica Bohemica},
keywords = {elliptic equation; discontinuous coefficient; a priori bound},
language = {eng},
number = {4},
pages = {507-515},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some $L^\{p\}$-estimates for solutions of elliptic equations in unbounded domains},
url = {http://eudml.org/doc/271827},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Monsurrò, Sara
AU - Transirico, Maria
TI - On some $L^{p}$-estimates for solutions of elliptic equations in unbounded domains
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 507
EP - 515
AB - In this review article we present an overview on some a priori estimates in $L^p$, $p>1$, recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two $L^p$-bounds, $p>2$, for the solution of the associated Dirichlet problem, obtained in correspondence with two different sign assumptions. Then, putting together the above mentioned bounds and using a duality argument, we extend the estimate also to the case $1<p<2$, for each sign assumption, and for a data in $L^p\cap L^2$.
LA - eng
KW - elliptic equation; discontinuous coefficient; a priori bound
UR - http://eudml.org/doc/271827
ER -

References

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