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On viscosity solutions for nontotally parabolic fully nonlinear equations

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Abstract

It is shown how to prove global unique solvability of the first initial-boundary value problem in the class of continuous viscosity solutions for some classes of equations −ut+F(ux,uxx)=g(x, t, ux), where F(p, A) is elliptic only on some nonlinear subsets of values of the arguments (p, A). For this purpose we use the techniques developed in the theory of viscosity solutions for degenerate elliptic equations. Bibliography: 12 titles.

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References

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Authors
  1. O. A. Ladyzhenskaya
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Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 112–130.

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Ladyzhenskaya, O.A. On viscosity solutions for nontotally parabolic fully nonlinear equations. J Math Sci 93, 697–710 (1999). https://doi.org/10.1007/BF02366848

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  • DOI: https://doi.org/10.1007/BF02366848

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