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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.