A priori estimates and smoothness of solutions of a~system of quasi-linear equations that is elliptic in the~Douglis--Nirenberg sense
Sbornik. Mathematics, Tome 187 (1996) no. 1, pp. 15-38
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We study a Douglis–Nirenberg elliptic system of quasi-linear equations. We solve the problem of the limiting admissible rate of growth of the non-linear terms of the system with respect to their arguments consistent with the possibility of obtaining estimates of the derivatives of a solution in terms of its maximum absolute value. The restrictions on the smoothness of the non-linear terms are minimal and the results are sharp. We construct an example that shows the optimality of the upper bound for the exponent of growth. A priori $L_p$-estimates are obtained both inside the domain for solutions belonging to certain Sobolev spaces. We obtain estimates of the Hölder norms of the derivatives of a solutions. We prove a theorem on a removable isolated singularity of bounded solutions of general elliptic systems of quasi-linear equation. All results are new, even for a single second-order equation.
@article{SM_1996_187_1_a1,
author = {G. V. Grishina},
title = {A priori estimates and smoothness of solutions of a~system of quasi-linear equations that is elliptic in {the~Douglis--Nirenberg} sense},
journal = {Sbornik. Mathematics},
pages = {15--38},
publisher = {mathdoc},
volume = {187},
number = {1},
year = {1996},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1996_187_1_a1/}
}
TY - JOUR AU - G. V. Grishina TI - A priori estimates and smoothness of solutions of a~system of quasi-linear equations that is elliptic in the~Douglis--Nirenberg sense JO - Sbornik. Mathematics PY - 1996 SP - 15 EP - 38 VL - 187 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1996_187_1_a1/ LA - en ID - SM_1996_187_1_a1 ER -
%0 Journal Article %A G. V. Grishina %T A priori estimates and smoothness of solutions of a~system of quasi-linear equations that is elliptic in the~Douglis--Nirenberg sense %J Sbornik. Mathematics %D 1996 %P 15-38 %V 187 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1996_187_1_a1/ %G en %F SM_1996_187_1_a1
G. V. Grishina. A priori estimates and smoothness of solutions of a~system of quasi-linear equations that is elliptic in the~Douglis--Nirenberg sense. Sbornik. Mathematics, Tome 187 (1996) no. 1, pp. 15-38. http://geodesic.mathdoc.fr/item/SM_1996_187_1_a1/