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1971•Russian Mathematical SurveysRequires access

THE PARAMETRIX OF ELLIPTIC OPERATORS WITH INFINITELY MANY INDEPENDENT VARIABLES

M. I. Vishik

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Abstract

Among the differential equations with infinitely many independent variables most attention has been paid to second-order parabolic equations. The paper begins with a brief review of the results obtained for the Cauchy problem for such equations. The parametrix is constructed for a certain class of elliptic differential operators with infinitely many variables. This parametrix is generated by a measure in the corresponding function space. A composition formula for an elliptic differential operator and its parametrix is proved. Applications are given to the theory of the solubility of elliptic equations with infinitely many variables.

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What this paper is about

Among the differential equations with infinitely many independent variables most attention has been paid to second-order parabolic equations. The paper begins with a brief review of the results obtained for the Cauchy problem for such equations. The parametrix is constructed for a certain class of elliptic differential operators with infinitely many variables. This parametrix is generated by a measure in the corresponding function space. A composition formula for an elliptic differential operator and its parametrix is proved. Applications are given to the theory of the solubility of elliptic equations with infinitely many variables.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Among the differential equations with infinitely many independent variables most attention has been paid to second-order parabolic equations. The paper begins with a brief review of the results obtained for the Cauchy problem for such equations. The parametrix is constructed for a certain class of elliptic differential operators with infinitely many variables. This parametrix is generated by a measure in the corresponding function space. A composition formula for an elliptic differential operator and its parametrix is proved. Applications are given to the theory of the solubility of elliptic equations with infinitely many variables.

Key concepts: Parametrix, Mathematics, Elliptic operator, Semi-elliptic operator, Elliptic partial differential equation, Mathematical analysis, Pure mathematics, Differential operator

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