Geodesic
On the optimal growth of functions with bounded Laplacian
Electronic journal of differential equations, Tome 2000 (2000)
Using a compactness argument, we introduce a Phragmen Lindelof type theorem for functions with bounded Laplacian. The technique is very useful in studying unbounded free boundary problems near the infinity point and also in approximating integrable harmonic functions by those that decrease rapidly at infinity. The method is flexible in the sense that it can be applied to any operator which admits the standard elliptic estimate.
Classification : 35J05, 35J60, 31C45
Keywords: optimal growth, bounded Laplacian, linear and semi-linear operators, capacity density condition 
@article{EJDE_2000__2000__a36,
     author = {Karp,  Lavi and Shahgholian,  Henrik},
     title = {On the optimal growth of functions with bounded {Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0937.35029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a36/}
}
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Karp,  Lavi; Shahgholian,  Henrik. On the optimal growth of functions with bounded Laplacian. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a36/