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Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
Harmonic maps nonlinear elliptic PDE’s regularity of solutions
2011/1/20
We consider nonlocal linear Schr¨odinger-type critical systems of the type 1/4v = v in IR. (1) where is antisymmetric potential in L2(IR, so(m)), v is a IRm valued map and
v denotes the matrix mu...
Variation formulas for principal functions (II) Applications to variation for harmonic spans
pseudoconvexity Stein manifold Riemann surface
2011/1/17
For a domain D in Cz with smooth boundary and for a, b ∈ D, a 6= b, we have the circular (radial) slit mapping P(z)(Q(z)) on D such that P(z) − 1 z−a (Q(z) − 1 z−a ) is regular...
Ito diffusions, modified capacity and harmonic measure. Applications to Schrodinger operators
Absolutely continuous spectrum Schr¨odinger operator
2011/2/22
We observe that some special Itˆo diffusions are related to scattering properties of a Schr¨odinger operator on Rd, d 2. We introduce Feynman-Kac type formulae for these stochastic processes wh...
A new formula for some linear stochastic equations with applications
Linear stochastic equation growth collapse process risk process
2010/12/8
We give a representation of the solution for a stochastic linear equation of the form Xt = Yt + R(0,t]Xs− dZs where Z is a c`adl`ag semimartingale and Y is a c`adl`ag adapted process with bounde...