JournalsaihpcVol. 12, No. 5pp. 507–575

Nonlinear oblique boundary value problems for Hessian equations in two dimensions

  • John Urbas

    Centre for Mathematics and Its Applications, GPO Box 4, Australian National University, Canberra, A.C.T. 0200 Australia
Nonlinear oblique boundary value problems for Hessian equations in two dimensions cover
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Abstract

We study nonlinear oblique boundary value problems for nonuniformly elliptic Hessian equations in two dimensions. These are equations whose principal part is given by a suitable symmetric function of the eigenvalues of the Hessian matrix D2u of the solution u. An interesting feature of our second derivative estimates is the need for certain strong structural hypotheses on the boundary condition, which are not needed in the uniformly elliptic case. Restrictions of this type are natural in our context; we present examples showing that second derivative bounds may fail if we do not assume such conditions.

Cite this article

John Urbas, Nonlinear oblique boundary value problems for Hessian equations in two dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), no. 5, pp. 507–575

DOI 10.1016/S0294-1449(16)30150-0