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تسجيل مستخدم جديدOn strong solutions of It^os equations with a$,in W^{1}_{d}$ and b$,in L_{d}$
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تأليف
N.V. Krylov
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We consider It^o 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 Holder 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.
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