Geodesic
Oblique derivative problem for elliptic equations in non-divergence form with $VMO$ coefficients
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 537-556

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A priori estimates and strong solvability results in Sobolev space $W^{2,p}(\Omega)$, $1$ are proved for the regular oblique derivative problem $$ \begin{cases} \sum_{i,j=1}^n a^{ij}(x)\frac{\partial^2u}{\partial x_i\partial x_j} =f(x) \text{ a.e. } \Omega \\ \frac{\partial u}{\partial \ell}+\sigma(x)u =\varphi(x) \text{ on } \partial \Omega \end{cases} $$ when the principal coefficients $a^{ij}$ are $V\kern -1.2pt MO\cap L^\infty$ functions.
Classification : 35J25
Keywords: oblique derivative; elliptic equation; non divergence form; $V\kern -1.2pt MO$ coefficients; strong solution 
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     author = {di Fazio, G. and Palagachev, D. K.},
     title = {Oblique derivative problem for elliptic equations in non-divergence form with $VMO$ coefficients},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {537--556},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {1996},
     mrnumber = {1426919},
     zbl = {0881.35028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a11/}
}
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di Fazio, G.; Palagachev, D. K. Oblique derivative problem for elliptic equations in non-divergence form with $VMO$ coefficients. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 537-556. http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a11/