A PRIORI ESTIMATE AND SOME PROPERTIES OF SOLUTIONS OF ELLIPTIC AND PARABOLIC EQUATIONS.
APL Library bulletin,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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In this paper we establish a priori estimates and costudy certain qualitative properties of generalized solutions of second-order elliptic and parabolic equations. The first fundamental results in this direction for equations with many independent variables were established in the papers by de Giorgi and Nash. A refined new approach to the consideration of similar problems and, in particular, a new proof of the de Giorgio theorem were given by Moser. In the present paper the method proposed by Moser is expanded.
- Theoretical Mathematics