Hölder Regularity For Integro-Differential Equations With Nonlinear Directional Dependence

Integro-partial differential equations with singular terminal condition

In this paper, we show that the minimal solution of a backward stochastic differential equation gives a probabilistic representation of the minimal viscosity solution of an integro-partial differential equation both with a singular terminal condition. Singularity means that at the final time, the value of the solution can be equal to infinity. Different types of regularity of this viscosity solution are investigated: Sobolev, H{ö}lder or strong regularity.

A localization of the L{é}vy operators arising in mathematical finances

The comparison principle and the existence of the solution of the integro-differential equation with L{é}vy operators, in the framework of the viscosity solution, are shown in this paper. For the one dimensional case, a detailed estimate of the H{ö}lder continuity of solutions is presented, by localizing the singularity of the L{é}vy measure.

超线性哈密顿量的非局部Hamilton-Jacobi方程的改进正则性

Improved Regularity for Nonlocal Hamilton--Jacobi Equations with Superlinear Hamiltonians

研究一类由x依赖积分微分算子和强制超线性哈密顿量驱动的非局部Hamilton-Jacobi方程的粘性解正则性，在一般结构假设下建立Hölder正则性，并在弱椭圆性条件下证明全局Lipschitz连续性，通过反例说明假设的尖锐性。

非退化稳定算子的边界正则性与Hopf引理

Boundary regularity and Hopf lemma for nondegenerate stable operators

本文针对满足外部C^{1,dini}性质的有界开集，证明了非退化稳定积分微分算子方程解的尖锐边界Hölder正则性与Hopf型边界引理，并展示了估计在s→1-时的稳健性，从而恢复二阶方程经典结果。

On the maximum principles and the quantitative version of the Hopf lemma for uniformly elliptic integro-differential operators

In the present paper we prove estimates on {subsolutions of the equation $-Av+c(x)v=0$}, $x\in D$, where $D\subset \bbR^d$ is a domain (i.e. an open and connected set) and $A$ is an integro-differential operator of the Waldenfels type, whose differential part satisfies the uniform ellipticity condition on compact sets. In general, the coefficients of the operator need not be continuous but only bounded and Borel measurable. Some of our results may be considered "quantitative" versions of the Hopf lemma, as they provide the lower bound on the outward normal directional derivative at the maximum…