Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods

By Guy Barles, Samuel Biton, Mariane Bourgoing, Olivier Ley. 2003

49 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7ff666e3115134f1baa8efdba6dc1bb80393ab03

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Weak Solutions of Forward–Backward SDE's (2003, methodology): “For interested reader we refer to the standard references [8,16], and the recent paper [3] for some general discussions of the comparison principles for fully nonlinear PDEs.”
A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2009, unknown): “(·) σ· = σ(t,φ t(·),hp,J ·i),a· = σ·σT,b· = b(t,φ (·),hp,J·i) so that Fφ (t,x,p,X) = Tr[ax (hX,Jx ⊗Jxi +hp,Hxi)]+bx = Tr JxaxJ T x X +bx +Tr[ax hp,Hxi]. 8A condition of this type also appears also in [1]. 6 MICHAEL CARUANA, PETER FRIZ AND HARALD OBERHAUSER Hence Fφ (t,x,p,Y˜ )−Fφ (t,x,p,X) = Tr J˜xa”
Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2005, result): “Some related results can be found in Barles et al. [5, 4 ]. In [4], in addition to comparison results for PDEs, one can also flnd BSDEs based on Markov processes with jumps.”
Stability of translating solutions to mean curvature flow (2005, background): “tion 3 gives the proof of Theorem 1.1. Appendix A. Maximum principle via viscosity solutions A special case of a comparison principle by Guy Barles, Samuel Biton, Mariane Bourgoing and Olivier Ley in [3] is as follows: Theorem A.1. Let u1,u2 : Rn × [0,T] → R be viscosity solutions to graphical mean ”
Viscosity solutions of general viscous Hamilton–Jacobi equations (2013, background): “ed an idea based on the convexity of Hthat goes back at least to Barles and Perthame [7] and appears in a form closer to our argument in Da Lio and Ley [10]. See also Barles and Da Lio [6] as well as [11, 15, 2, 5], wherein special cases of the results presented in this section can also be found. Se”