We give a simple proof that the solution of the Allen-Cahn equation converges to Brakke's motion by mean curvature, by utilizing the recent results of Röger and Schätzle in space dimension 2 and 3.

We consider a rough differential equation indexed by a small parameter ε > 0. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter H (1/4 < H < 1/2), we ...

Discover how Einstein’s theory of special relativity reshaped physics by linking space, time, mass, and energy in a universe governed by the speed of light. Albert Einstein's 1905 theory of special ...