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A priori estimates for solutions of the first initial boundary-value problem for systems of fully nonlinear partial differential equations

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Abstract

We prove a priori estimates for a solution of the first initial boundary-value problem for a system of fully nonlinear partial differential equations (PDE) in a bounded domain. In the proof, we reduce the initial boundary-value problem to a problem on a manifold without boundary and then reduce the resulting system on the manifold to a scalar equation on the total space of the corresponding bundle over the manifold.

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Authors
  1. Ya. I. Belopol’skaya
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Additional information

St. Petersburg Architecture Building University, St. Petersburg. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 338–363, March, 1997.

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Belopol’skaya, Y.I. A priori estimates for solutions of the first initial boundary-value problem for systems of fully nonlinear partial differential equations. Ukr Math J 49, 373–402 (1997). https://doi.org/10.1007/BF02487240

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  • DOI: https://doi.org/10.1007/BF02487240

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