Viscosity solutions of fully nonlinear functional parabolic PDE
نویسندگان
چکیده
منابع مشابه
Viscosity solutions of fully nonlinear functional parabolic PDE
Here, Q = (0,T) ×Ω, Γ = (0,T) × ∂Ω (T < +∞ or T = +∞), and Ω is a bounded open subset ofRn, Qτ̄=[−τ̄,0]×Ω, Cm=C[−τ̄,0]×···×C[−τ̄,0] denotes the corresponding continuous function space; u : Qτ̄ ∪Q→R is the unknown function, ut(τ) = (ut(τ1), . . . , ut(τm)) = (u(t+ τ1,x), . . . ,u(t + τm,x)) with −τ̄ ≤ τj ≤ 0, j = 1,2, . . . ,m, f : Q×R×Cm × R×Rn× S(n) →R is a given functional which is locally bounded,...
متن کاملComparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs
We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi & Zhang [10], our conditions are easier to check and allow for the degenerate case, thus including first order path-dependent PDEs. Our argument follows the regularization method as introduced by Jensen, Lions & Sougani...
متن کاملUniqueness of Viscosity Solutions of a Geometric Fully Nonlinear Parabolic Equation
We observe that the comparison result of Barles-Biton-Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.
متن کاملViscosity Solutions of Fully Nonlinear Parabolic Path Dependent Pdes: Part I by Ibrahim Ekren,
The main objective of this paper and the accompanying one [Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012) Preprint] is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work [Ann. Probab. (2014) 42 204–236], focused on the semilinear case, and is crucially based on the nonlinear...
متن کاملContinuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Equations
Using the maximum principle for semicontinuous functions (Differential Integral Equations 3 (1990), 1001–1014; Bull. Amer. Math. Soc. (N.S) 27 (1992), 1–67), we establish a general ‘‘continuous dependence on the nonlinearities’’ estimate for viscosity solutions of fully nonlinear degenerate parabolic equations with timeand space-dependent nonlinearities. Our result generalizes a result by Souga...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2005
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms.2005.3539