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Flows generated by symmetric functions of the eigenvalues of the Hessian. (English) Zbl 0888.35056

Ladyzhenskaya, O. A. (ed.), Boundary value problems of mathematical physics and adjacent problems of function theory. 26. Work collection. Dedicated to N. N. Ural’tseva on her anniversary. Sankt-Peterburg: Nauka. Zap. Nauchn. Semin. POMI. 221, 127-144 (1995).
Summary: The global unique solvability of the first initial-boundary value problem for fully nonlinear equations of the form \[ -u_t+ f(\lambda_1[u],\dots, \lambda_n[u])= g \] is proved. Here, \(\lambda_i[u]\), \(i=1,\dots, n\), are eigenvalues of the Hessian \(u_{xx}\) and \(f\) is a symmetric function satisfying some conditions.
For the entire collection see [Zbl 0868.00020].

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)