JournalsaihpcVol. 6, No. 6pp. 419–435

Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order

  • Michael G. Crandall

    Department of Mathematics, University of California, Santa Barbara Santa Barbara, CA 93106
Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order cover
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Abstract

We study the function u(x)v(y)λ2xy2u(x)–v(y)−\frac{\mathrm{\lambda }}{2}\left\|x–y\right\|^{2} to second order, when u is u. s. c. and v is l. s. c., near a point (x\limits^{ˆ},y\limits^{ˆ}) where the maximum is attained. We obtain a sharpening of a result of P.-L. Lions and H. Ishii which implies comparison results for fully nonlinear elliptic equations of second order.

Résumé

On étudie au second ordre la fonction u(x)v(y)λ2xy2u(x)–v(y)−\frac{\mathrm{\lambda }}{2}\left\|x–y\right\|^{2}, quand u est s. c. s., v est s. c. i., au voisinage d’un point (x\limits^{ˆ},y\limits^{ˆ}) où elle atteint son maximum. On en déduit notamment des résultats de comparaison pour des équations elliptiques non linéaires du second ordre.

Cite this article

Michael G. Crandall, Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 6, pp. 419–435

DOI 10.1016/S0294-1449(16)30309-2