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Homogenization of Hamilton-Jacobi equations in the Heisenberg group
Free-boundary regularity for generalized porous medium equations
| 1. | Department of Mathematics, Columbia University, United States |
| 2. | Deaprtment of Mathematics, University of California at Irvine Irvine, CA., United States |
$u_t = \Delta \Phi(u)$ in R$^n \times [0,T]$
$u(x)=u_0(x)$ on R$^n$
with the nonlinearity $\Phi(u)$. For the case of $\Phi(u)=\sum_{i=1}^m c_i u^{\alpha_i}$, we show the existence of a solution which smoothness depends on the exponents $\alpha_i$. Regardless of the regularity of the solution, we show the free-boundary is smooth. We also extend similar results for $\Phi(u)$ as an infinite sum.
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