Existence of three solutions for quasilinear elliptic equations: an Orlicz-Sobolev space setting

2017 ◽  
Vol 33 (2) ◽  
pp. 287-296 ◽  
Author(s):  
Fei Fang ◽  
Zhong Tan
Keyword(s):  
Sobolev Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Three Solutions ◽  
Space Setting ◽  
Quasilinear Elliptic

scholarly journals Oblique derivative problem for quasilinear elliptic equations with VMO coefficients

1996 ◽  
Vol 53 (3) ◽  
pp. 501-513 ◽  
Author(s):  
Guiseppe Di Fazio ◽  
Dian K. Palagachev
Keyword(s):  
Sobolev Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Oblique Derivative Problem ◽  
Strong Solvability ◽  
Derivative Problem ◽  
Carathéodory Functions ◽  
Vmo Coefficients ◽  
Image Position ◽  
Quasilinear Elliptic

Strong solvability and uniqueness in the Sobolev space W2, q(Ω), q > n, are proved for the oblique derivative problemassuming the coefficients of the quasilinear elliptic operator to be Carathéodory functions, aij ∈ VMO∩L∞ with respect to x, and b to grow at most quadratically with respect to the gradient.

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