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20092026
most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations · 7.5k across the 146 of their papers we have counts for

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math.AP2016★ 14 cited

Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces

Adam Andersson, Mario Hefter, Arnulf Jentzen +1

In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diff…

math.AP2012★ 83 cited

Loss of regularity for Kolmogorov equations

Martin Hairer, Martin Hutzenthaler, Arnulf Jentzen

The celebrated Hörmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficient…