On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains

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  • Strong solutions to reflecting stochastic differential equations with singular drift

    2023, Stochastic Processes and their Applications
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    Now we can give the construction of the first class of test functions as follows. To construct the second class of test functions, let us recall the following result from Lemma 4.4 in [3]. We only give the proof of the last assertion because the proof of others are similar.

  • Stochastic and partial differential equations on non-smooth time-dependent domains

    2019, Stochastic Processes and their Applications
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    Here we generalize these test functions to our time-dependent setting, and obtain the corresponding results for both SDEs and PDEs in time-dependent domains. In particular, our PDE results generalize the main part of [11] to hold in the setting of fully nonlinear second-order parabolic PDEs in non-smooth time-dependent domains. Our proofs are based on the theory of viscosity solutions.

  • Limit theorems and the support of SDES with oblique reflections on nonsmooth domains

    2018, Journal of Mathematical Analysis and Applications
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    For the case reflected in domains neither smooth nor convex, Aida–Sasaki [1] considered the Wong–Zakai approximation and obtained the limit theorem. We begin this section with some properties of test functions for Case 1 and Case 2, more details of which are referred to [3] and [4]. Our main result in this sequel is

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Supported in part by grant No. AFOSR-85-0315 while visiting the Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI, U.S.A.

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