Geodesic
Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space
Izvestiya. Mathematics , Tome 61 (1997) no. 2, pp. 285-315

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

We introduce a scale of spaces that are dual to the classical Morrey space. We establish the solubility of non-linear elliptic systems on an interval of this scale, the range of the interval being essentially dependent on the modulus of ellipticity of the system. As a consequence, we prove solubility when the right-hand side is (1) a Lebesgue space with exponent weaker than the Sobolev exponent, (2) a space of densities of finite Borel measure, and (3) a Hardy space for $p\leqslant 1$ under certain restrictions on the modulus of ellipticity. We prove the existence and good behaviour of solutions of fundamental type. Our results are also completely new for linear systems with bounded discontinuous coefficients. 
@article{IM2_1997_61_2_a2,
     author = {E. A. Kalita},
     title = {Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space},
     journal = {Izvestiya. Mathematics },
     pages = {285--315},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a2/}
}
TY  - JOUR
AU  - E. A. Kalita
TI  - Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space
JO  - Izvestiya. Mathematics 
PY  - 1997
SP  - 285
EP  - 315
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a2/
LA  - en
ID  - IM2_1997_61_2_a2
ER  - 
%0 Journal Article
%A E. A. Kalita
%T Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space
%J Izvestiya. Mathematics 
%D 1997
%P 285-315
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a2/
%G en
%F IM2_1997_61_2_a2
E. A. Kalita. Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space. Izvestiya. Mathematics , Tome 61 (1997) no. 2, pp. 285-315. http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a2/