论文标题
在用$ \，\ in w^{1} _ {d} $和b $ \，\ in l_ {d} $中的$ \，\中
On strong solutions of Itô's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$
论文作者
论文摘要
我们认为ITô以时间独立系数为单一的非等级方程，$ W^{1} _ {D，LOC} $中的扩散系数和$ L_ {D} $中的漂移。我们证明了任何起点的独特强大解决性，并证明，作为起点的函数，解决方案与任何指数$ <1 $连续hölder是连续的。我们还证明，如果给我们一系列系数以适当的含义收敛到原始的系数，则近似方程的解决方案会收敛到原始溶液的解决方案。
We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{d,loc}$, and the drift in $L_{d}$. We prove the unique strong solvability for any starting point and prove that as a function of the starting point the solutions are Hölder continuous with any exponent $<1$. We also prove that if we are given a sequence of coefficients converging in an appropriate sense to the original ones, then the solutions of approximating equations converge to the solution of the original one.
