# Fully nonlinear second order elliptic equations with large zeroth order coefficient

L. C. Evans; Pierre-Louis Lions

Annales de l'institut Fourier (1981)

- Volume: 31, Issue: 2, page 175-191
- ISSN: 0373-0956

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topEvans, L. C., and Lions, Pierre-Louis. "Fully nonlinear second order elliptic equations with large zeroth order coefficient." Annales de l'institut Fourier 31.2 (1981): 175-191. <http://eudml.org/doc/74495>.

@article{Evans1981,

abstract = {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.},

author = {Evans, L. C., Lions, Pierre-Louis},

journal = {Annales de l'institut Fourier},

keywords = {nonlinear second order elliptic equations; existence of classical solutions; a priori estimate; continuation methods},

language = {eng},

number = {2},

pages = {175-191},

publisher = {Association des Annales de l'Institut Fourier},

title = {Fully nonlinear second order elliptic equations with large zeroth order coefficient},

url = {http://eudml.org/doc/74495},

volume = {31},

year = {1981},

}

TY - JOUR

AU - Evans, L. C.

AU - Lions, Pierre-Louis

TI - Fully nonlinear second order elliptic equations with large zeroth order coefficient

JO - Annales de l'institut Fourier

PY - 1981

PB - Association des Annales de l'Institut Fourier

VL - 31

IS - 2

SP - 175

EP - 191

AB - 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.

LA - eng

KW - nonlinear second order elliptic equations; existence of classical solutions; a priori estimate; continuation methods

UR - http://eudml.org/doc/74495

ER -

## References

top- [1] L. C. EVANS, On solving certain nonlinear partial differential equations by accretive operator methods, to appear in Isr. J. Math., (1981). Zbl0454.35038
- [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. Zbl0425.35046MR80f:93091
- [3] A. FRIEDMAN, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. Zbl0224.35002MR56 #3433
- [4] O. A. LADYŽEWSKAJA and N. N. URAL'CEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002
- [5] P. L. LIONS, Résolution des problèmes de Bellman-Dirichlet, to appear in Acta Math., (1981). Zbl0467.49016MR83c:49038
- [6] P. L. LIONS, Résolution de problèmes elliptiques quasilinéaires, Arch. Rat. Mech. Anal., 74 (1980), 335-354. Zbl0449.35036MR82a:35034
- [7] I. V. SKRYPNIK, On the topological character of general nonlinear operators, Doklady, 239 (1978), 538-541 (Russian). Zbl0393.35031MR58 #6678

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