Fully nonlinear second order elliptic equations with large zeroth order coefficient
Annales de l'Institut Fourier, Volume 31 (1981) no. 2, p. 175-191

We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an a priori estimate asserting that the ${C}^{2,\alpha }$-norm of the solution cannot lie in a certain interval of the positive real axis.

On démontre l’existence de solutions classiques pour certaines équations elliptiques du deuxième ordre, fortement non linéaires, ayant des coefficients d’ordre zéro assez grands. On utilise essentiellement une estimation a priori impliquant que la norme ${C}^{2,\alpha }$ de la solution ne peut appartenir à un intervalle de la demi-droite réelle positive.

@article{AIF_1981__31_2_175_0,
author = {Evans, L. C. and Lions, Pierre-Louis},
title = {Fully nonlinear second order elliptic equations with large zeroth order coefficient},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Durand},
address = {28 - Luisant},
volume = {31},
number = {2},
year = {1981},
pages = {175-191},
doi = {10.5802/aif.834},
zbl = {0441.35023},
mrnumber = {82m:35047},
language = {en},
url = {http://www.numdam.org/item/AIF_1981__31_2_175_0}
}

Evans, L. C.; Lions, Pierre-Louis. Fully nonlinear second order elliptic equations with large zeroth order coefficient. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 175-191. doi : 10.5802/aif.834. http://www.numdam.org/item/AIF_1981__31_2_175_0/

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