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In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
Free boundary problems have vast and important applications in physics, mechanics, biology, engineering, and finance, etc. At the same time, there is a great challenge in their mathematical study whic...
This conference is the 14th International Conference on Free Boundary Problems: Theory and Applications, which is in the series of conferences beginning in Montecatini (Italy, 1981) and succeeding in ...
Free boundary problems of the Euler equation: local well-posedness and hydrodynamical instabilities.
In this paper we study a free boundary problem modeling the growth of solid tumors. Due to the free boundary and surface tension effects, this problem is a nonlinear problem involving non-local terms....
We consider n-dimensional hypersurfaces flowing by mean curvature flow with Neumann free boundary conditions supported on a smooth support surface. We show that the Hausdorff n-measure of the singula...
In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing f...
Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root ...
A gradient bound for free boundary graphs      gradient bound f  free boundary graphs        font style='font-size:12px;'> 2010/12/10
We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free b...
We consider an American put option under the CEV process. This corre-sponds to a free boundary problem for a PDE. We show that this free boundary satis es a nonlinear integral equation, and analyze it...

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