A Variational Approach to Image Inpainting and Text Removal

Author(s):  
Japhet Niyobuhungiro ◽  
Froduald Minani ◽  
Fredrik Berntsson ◽  
George Baravdish
Author(s):  
HONG-CHANG SHIN ◽  
Gwangsoon Lee ◽  
Ho min Eum ◽  
Jeong-Il Seo

2013 ◽  
Vol 33 (12) ◽  
pp. 3536-3539
Author(s):  
Donghai ZHAI ◽  
Wenjie ZUO ◽  
Weixia DUAN ◽  
Jiang YU ◽  
Tongliang LI

2013 ◽  
Vol 26 (3) ◽  
pp. 248-254
Author(s):  
Chun Liu ◽  
Zhiwei Kang ◽  
Yigang He

Author(s):  
Shaya Shakerian

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].


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