Ramzi Alsaedi, Habib Maagli, Noureddine Zeddini
Abstract:
We give global estimates on some potential of functions in a bounded domain
of the Euclidean space
. These functions
may be singular near the boundary and are globally comparable to a product
of a power of the distance to the boundary by some particularly well behaved
slowly varying function near zero. Next, we prove the existence and uniqueness
of a positive solution for the integral equation
with
,
where V belongs to a class of kernels that contains
in particular the potential kernel of the classical Laplacian
or the fractional laplacian
,
.
Submitted September 14, 2013. Published January 7, 2014.
Math Subject Classifications: 35R11, 35B40, 35J08.
Key Words: Green function; Dirichlet Laplacian; fractional Laplacian;
Karamata function.
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Ramzi Alsaedi Department of Mathematics, College of Sciences and Arts King Abdulaziz University, Rabigh Campus P.O. Box 344, Rabigh 21911, Saudi Arabia email: ramzialsaedi@yahoo.co.uk | |
Habib Mâagli Department of Mathematics, College of Sciences and Arts King Abdulaziz University, Rabigh Campus P.O. Box 344, Rabigh 21911, Saudi Arabia email: habib.maagli@fst.rnu.tn | |
Noureddine Zeddini Department of Mathematics, College of Sciences and Arts King Abdulaziz University, Rabigh Campus P.O. Box 344, Rabigh 21911, Saudi Arabia email: noureddine.zeddini@ipein.rnu.tn |
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