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Solvability of the first boundary value problem for higher order quasilinear elliptic equations which degenerate with respect to the independent variables

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Abstract

For a class of quasilinear elliptic equations of an arbitrary order, admitting a fixed weak degeneracy with respect to the independent variables, one proves an existence theorem for the generalized solution of the Dirichlet problem. On gives conditions under which such a solution is unique.

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Literature cited

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 96, pp. 187–204, 1980.

The author expresses his gratitude to A. V. Ivanov for his constant interest in the paper and for repeated discussions.

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Mkrtychyan, P.Z. Solvability of the first boundary value problem for higher order quasilinear elliptic equations which degenerate with respect to the independent variables. J Math Sci 21, 783–797 (1983). https://doi.org/10.1007/BF01094441

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Keywords

  • Generalize Solution
  • Elliptic Equation
  • Dirichlet Problem
  • Existence Theorem
  • Arbitrary Order