Geodesic
On Quasilinear Beltrami-Type Equations with Degeneration
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 445-453

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the solvability problem for the equation $f_{\overline{z}}=\nu(z,f(z)) f_z$, where the function $\nu(z,w)$ of two variables can be close to unity. Such equations are called quasilinear Beltrami-type equations with ellipticity degeneration. We prove that, under some rather general conditions on $\nu(z,w)$, the above equation has a regular homeomorphic solution in the Sobolev class $W_{\operatorname{loc}}^{1,1}$. Moreover, such solutions $f$ satisfy the inclusion $f^{\,-1}\in W_{\operatorname{loc}}^{1,2}$.
Keywords: quasilinear Beltrami-type equation, existence theorem, regular homeomorphic solution, Sobolev class, homeomorphism, Carathéodory condition, function of bounded mean oscillation. 
@article{MZM_2011_90_3_a9,
     author = {E. A. Sevost'yanov},
     title = {On {Quasilinear} {Beltrami-Type} {Equations} with {Degeneration}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {445--453},
     publisher = {mathdoc},
     volume = {90},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a9/}
}
TY  - JOUR
AU  - E. A. Sevost'yanov
TI  - On Quasilinear Beltrami-Type Equations with Degeneration
JO  - Matematičeskie zametki
PY  - 2011
SP  - 445
EP  - 453
VL  - 90
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a9/
LA  - ru
ID  - MZM_2011_90_3_a9
ER  - 
%0 Journal Article
%A E. A. Sevost'yanov
%T On Quasilinear Beltrami-Type Equations with Degeneration
%J Matematičeskie zametki
%D 2011
%P 445-453
%V 90
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a9/
%G ru
%F MZM_2011_90_3_a9
E. A. Sevost'yanov. On Quasilinear Beltrami-Type Equations with Degeneration. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 445-453. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a9/