Nonlinear Analysis: Theory, Methods & Applications
On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains
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Cited by (40)
Strong solutions to reflecting stochastic differential equations with singular drift
2023, Stochastic Processes and their ApplicationsCitation Excerpt :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.
On the equivalence of viscosity and distribution solutions of second-order PDEs with Neumann boundary conditions
2020, Stochastic Processes and their ApplicationsStochastic and partial differential equations on non-smooth time-dependent domains
2019, Stochastic Processes and their ApplicationsCitation Excerpt :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 ApplicationsCitation Excerpt :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
Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions
2011, Journal des Mathematiques Pures et AppliqueesA convergence result for the ergodic problem for Hamilton-Jacobi equations with Neumann-type boundary conditions
2016, Proceedings of the Royal Society of Edinburgh Section A: Mathematics
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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.