# 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

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topMonsurrò, 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 -

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