On Lp-Estimates of Optimal Type for the Parabolic Oblique Derivative Problem with VMO-Coefficients — A Refined Version

2006 ◽  
pp. 529-536
Author(s):  
Peter Weidemaier
Keyword(s):  
Oblique Derivative Problem ◽  
Lp Estimates ◽  
Derivative Problem ◽  
Vmo Coefficients ◽  
Optimal Type ◽  
Refined Version

scholarly journals Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 49-61
Author(s):  
Vagif S. Guliyev ◽  
Mehriban N. Omarova
Keyword(s):  
Morrey Space ◽  
Discontinuous Coefficients ◽  
Morrey Spaces ◽  
Oblique Derivative Problem ◽  
Derivative Problem ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Vmo Coefficients ◽  
Generalized Weighted Morrey Space ◽  
The Right

AbstractWe obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space $\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.

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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