Partial regularity for quasilinear nonuniformly elliptic systems of the total type
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 62-70
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We establish partial $C^{1,\alpha}$-regularity of weak solutions of
nonhomogeneous nondiagonal nonuniformly elliptic systems of the
type
$$
-\partial/\partial x_\alpha A^i_\alpha(x,u,u_x)=B^i(x,u,u_x),\quad i=1,\dots,N.
$$
The typical example of admissible systems is the system of the
Euler equations of the variational problem on a minimum of integral
$\int_\Omega\mathcal{F}(u_x)d\,x$ with the integrand of the type
$$
\mathcal{F}(p)=a|p|^2+b|p|^m+\sqrt{1+\mathrm{det}^2p},\quad a>0,\ b>0,
$$
if $b$ is sufficiently large.
@article{ZNSL_1992_200_a5,
author = {A. V. Ivanov and M. Frasca},
title = {Partial regularity for quasilinear nonuniformly elliptic systems of the total type},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {62--70},
publisher = {mathdoc},
volume = {200},
year = {1992},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a5/}
}
TY - JOUR AU - A. V. Ivanov AU - M. Frasca TI - Partial regularity for quasilinear nonuniformly elliptic systems of the total type JO - Zapiski Nauchnykh Seminarov POMI PY - 1992 SP - 62 EP - 70 VL - 200 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a5/ LA - ru ID - ZNSL_1992_200_a5 ER -
A. V. Ivanov; M. Frasca. Partial regularity for quasilinear nonuniformly elliptic systems of the total type. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 62-70. http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a5/