Parabolic comparison revisited and applications

Joscha Diehl; Peter K. Friz; Harald Oberhauser

Parabolic comparison revisited and applications

Analysis of PDEs 2011-03-01 v1 Probability

Authors: Joscha Diehl , Peter K. Friz , Harald Oberhauser

Abstract

We consider the Cauchy-Dirichlet problem $\partial_t u - F(t,x,u,Du,D^2 u) = 0 on (0,T)\times \R^n$ in viscosity sense. Comparison is established for bounded semi-continuous (sub-/super-)solutions under structural assumption (3.14) of the User's Guide plus a mild condition on $F$ such as to cope with the unbounded domain. Comparison on $(0,T]$ , space-time regularity and existence are also discussed. Our analysis passes through an extension of the parabolic theorem of sums which appears to be useful in its own right.

Keywords

parabolic equations parabolic partial differential equations cauchy problem

Cite

@article{arxiv.1102.5774,
  title  = {Parabolic comparison revisited and applications},
  author = {Joscha Diehl and Peter K. Friz and Harald Oberhauser},
  journal= {arXiv preprint arXiv:1102.5774},
  year   = {2011}
}

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