We prove an integral estimate for weak solutions to some quasilinear elliptic systems; such an estimate provides us with the following regularity result: weak solutions are bounded.
@article{116941, author = {Francesco Leonetti}, title = {An integral estimate for weak solutions to some quasilinear elliptic systems}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {39-43}, zbl = {0751.35009}, mrnumber = {1118288}, language = {en}, url = {http://dml.mathdoc.fr/item/116941} }
Leonetti, Francesco. An integral estimate for weak solutions to some quasilinear elliptic systems. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 39-43. http://gdmltest.u-ga.fr/item/116941/
Elliptic systems with nonlinearity $q$ greater or equal to two. Regularity of the solution of the Dirichlet problem, Ann. Mat. Pura Appl. 147 (1987), 117-150. (1987) | MR 0916705 | Zbl 0635.35038
Fundamental interior estimates for a class of second order elliptic operators, in: Partial Differential Equations and Calculus of Variations, Essays in honor of Ennio De Giorgi, Birkhäuser, Boston, 1989. | MR 1034007 | Zbl 0685.35026
Partial regularity for minimizers of certain functionals having non quadratic growth, Ann. Mat. Pura Appl. 155 (1989), 1-24. (1989) | MR 1042826
Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton University Press, Princeton, 1983. | MR 0717034 | Zbl 0516.49003
On the regularity of $w$-minima, to appear in Boll. Un. Mat. Ital.
Multiple Integrals in the Calculus of Variations, Springer Verlag, New York, 1966. | MR 0202511