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

Abstract

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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.

How to cite

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Evans, 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

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  1. [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. [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. [3] A. FRIEDMAN, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. Zbl0224.35002MR56 #3433
  4. [4] O. A. LADYŽEWSKAJA and N. N. URAL'CEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002
  5. [5] P. L. LIONS, Résolution des problèmes de Bellman-Dirichlet, to appear in Acta Math., (1981). Zbl0467.49016MR83c:49038
  6. [6] P. L. LIONS, Résolution de problèmes elliptiques quasilinéaires, Arch. Rat. Mech. Anal., 74 (1980), 335-354. Zbl0449.35036MR82a:35034
  7. [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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