L 1 - uniqueness of degenerate elliptic operators

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Parametrix Techniques and Martingale Problems for Some Degenerate Kolmogorov Equations

We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins [2] to prove uniqueness of the martingale problem in the framework of non-degenerate elliptic operators and the Mc Kean and Singer [13] parametrix approach to the density expansion that has previously ...

J an 2 00 6 The submartingale problem for a class of degenerate elliptic operators Richard

We consider the degenerate elliptic operator acting on C2 functions on [0,∞)d: Lf(x) = d ∑ i=1 ai(x)x αi i ∂2f ∂xi (x) + d ∑ i=1 bi(x) ∂f ∂xi (x), where the ai are continuous functions that are bounded above and below by positive constants, the bi are bounded and measurable, and the αi ∈ (0, 1). We impose Neumann boundary conditions on the boundary of [0,∞)d. There will not be uniqueness for th...

Degenerate Diffusion Operators Arising in Population Biology

We analyze a class of partial differential equations that arise as"backwards Kolmogorov operators"in infinite population limits of the Wright-Fisher models in population genetics and in mathematical finance. These are degenerate elliptic operators defined on manifolds with corners. The classical example is the Kimura diffusion operator, which acts on functions defined on the simplex in R^n. We ...

Quasilinear Degenerate Evolution Equations in Banach Spaces

The quasilinear degenerate evolution equation of parabolic type d(Mv) dt + L(Mv)v = F (Mv), 0 < t ≤ T considered in a Banach space X is written, putting Mv = u, in the form du dt + A(u)u 3 F (u), 0 < t ≤ T , where A(u) = L(u)M−1 are multivalued linear operators in X for u ∈ K, K being a bounded ball ‖u‖Z < R in another Banach space Z continuously embedded in X. Existence and uniqueness of the l...