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

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,α de la solution ne peut appartenir à un intervalle de la demi-droite réelle positive.

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,α -norm of the solution cannot lie in a certain interval of the positive real axis.

@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},
     pages = {175--191},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     number = {2},
     year = {1981},
     doi = {10.5802/aif.834},
     mrnumber = {82m:35047},
     zbl = {0441.35023},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.834/}
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Evans, L. C.; Lions, Pierre-Louis. Fully nonlinear second order elliptic equations with large zeroth order coefficient. Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 175-191. doi : 10.5802/aif.834. http://www.numdam.org/articles/10.5802/aif.834/

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