no. 2
Fully nonlinear second order elliptic equations with large zeroth order coefficient
Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 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,α -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,α 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},
     pages = {175--191},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     number = {2},
     year = {1981},
     doi = {10.5802/aif.834},
     zbl = {0441.35023},
     mrnumber = {82m:35047},
     language = {en},
     url = {https://aif.centre-mersenne.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, Volume 31 (1981) no. 2, pp. 175-191. doi : 10.5802/aif.834. https://aif.centre-mersenne.org/articles/10.5802/aif.834/

[1] L. C. Evans, On solving certain nonlinear partial differential equations by accretive operator methods, to appear in Isr. J. Math., (1981). | Zbl

[2] L. C. Evans and A. Friedman, Stochastic optimal switching and the Dirichlet problem for the Bellman equation, Trans. Am. Math. Soc., 253 (1979), 365-389. | MR | Zbl

[3] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. | MR | Zbl

[4] O. A. Ladyžewskaja and N. N. Ural'Ceva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. | Zbl

[5] P. L. Lions, Résolution des problèmes de Bellman-Dirichlet, to appear in Acta Math., (1981). | MR | Zbl

[6] P. L. Lions, Résolution de problèmes elliptiques quasilinéaires, Arch. Rat. Mech. Anal., 74 (1980), 335-354. | MR | Zbl

[7] I. V. Skrypnik, On the topological character of general nonlinear operators, Doklady, 239 (1978), 538-541 (Russian). | MR | Zbl

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