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.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMUC_1996__37_3_a11,
     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/}
}
TY  - JOUR
AU  - di Fazio, G.
AU  - Palagachev, D. K.
TI  - Oblique derivative problem for elliptic equations in non-divergence form with $VMO$ coefficients
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1996
SP  - 537
EP  - 556
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a11/
LA  - en
ID  - CMUC_1996__37_3_a11
ER  - 
%0 Journal Article
%A di Fazio, G.
%A Palagachev, D. K.
%T Oblique derivative problem for elliptic equations in non-divergence form with $VMO$ coefficients
%J Commentationes Mathematicae Universitatis Carolinae
%D 1996
%P 537-556
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a11/
%G en
%F CMUC_1996__37_3_a11
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/