We introduce the notion of generalized solutions for Hessian equations. Such a definition is given in the class of semi-convex functions, and it extends the definition of convex generalised solutions for the Monge-Ampere equation. We prove that semiconvex weak solutions are solutions in the sense of the present paper.
Generalized solutions of Hessian equations / A. Colesanti; P. Salani. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 56 n. 3:(1997), pp. 459-466.
Generalized solutions of Hessian equations
COLESANTI, ANDREA;SALANI, PAOLO
1997
Abstract
We introduce the notion of generalized solutions for Hessian equations. Such a definition is given in the class of semi-convex functions, and it extends the definition of convex generalised solutions for the Monge-Ampere equation. We prove that semiconvex weak solutions are solutions in the sense of the present paper.
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