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On the Existence of a Generalized Solution of One Partial Differential System

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Abstract

We propose a method for the construction of generalized solutions for some nondivergent partial differential systems using set-valued analogs of the generalized statement of the problem based on subdifferential calculus. We establish new sufficient conditions for the existence of solutions of a variational inequality with set-valued operator under weakened coerciveness conditions. We consider examples of a weighted p-Laplacian in the Sobolev spaces \(W_p^1 \left( \Omega \right)\), p ≥ 2.

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Authors and Affiliations

  1. “KPI” National Technical University, Kiev

    O. V. Solonukha

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  1. O. V. Solonukha
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Solonukha, O.V. On the Existence of a Generalized Solution of One Partial Differential System. Ukrainian Mathematical Journal 54, 1509–1525 (2002). https://doi.org/10.1023/A:1023420019661

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