Abstract

We consider a sequence of matrices ah(x,t)a_h(x,t) whose minimum eigenvalue is a positive function λh(x)\lambda_h(x) and the maximum one is Lλh(x)L\lambda_h(x), λh\lambda_h satisfying a uniform Muckenhoupt's condition. We study G-convergence of the sequence of linear parabolic operators in divergence form associated to these matrices and with coefficient λh\lambda_h in front of the temporal derivative. When the matrices are depending only on the variable x we compare this result with the analogous results for the sequence of elliptic operators and the sequence of standard parabolic operators associated to the same sequence of matrices.

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Keywords

  • Jumping problems
  • variational inequalities
  • nonsmooth critical point theory

Mathematics Subject Classification

35D05; 58J05

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Suggested citation

F. Paronetto. “Some New Results on the Convergence of Degenerate Elliptic and Parabolic Equations.” Journal of Convex Analysis 9 (2002), No. 1, 31–54. https://doi.org/10.68381/jca09002

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press LLC.