The obstacle problem for nonlinear integro-differential operators

Obstacle Problem for Nonlinear Integro{differential Equations Arising in Option Pricing

Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

Obstacle problems for integro-differential operators: regularity of solutions and free boundaries

We study the obstacle problem for integro-differential operators of order 2s, with s ∈ (0, 1). Our main result establishes that the free boundary is C and u ∈ C near all regular points. Namely, we prove the following dichotomy at all free boundary points x0 ∈ ∂{u = φ}: (i) either u(x)− φ(x) = c d(x) + o(|x− x0|) for some c > 0, (ii) or u(x)− φ(x) = o(|x− x0|), where d is the distance to the con...

Nonlinear Integro - Differential Equations

Trace Formulae for Matrix Integro-Differential Operators

where λ is a spectral parameter, Y (x) = [yk(x)]k=1,d is a column vector, Q(x) and M(x, t) are d×d real symmetric matrix-valued functions, and h and H are d×d real symmetric constant matrices. M(x, t) is an integrable function on the set D0 def ={(x, t) : 0≤ t ≤ x ≤ π, x, t ∈ R}, Q ∈ C1[0,π], where C1[0,π] denotes a set whose element is a continuously differentiable function on [0,π]. In partic...