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2 questions
4
votes
1
answer
162
views
Uniqueness of critical points for Lipschitz perturbations of uniformly convex Hamiltonians
Consider a macroscopic free energy functional of the form
$$\mathcal{F}_\beta(\mu):= \frac{1}{\beta}\int_{\mathbb{R}^d}\log(\mu)\mu dx + \int_{\mathbb{R}^d}V(x)\mu(x)dx + \iint_{(\mathbb{R}^d)^2}g(x-y)...
- 873
5
votes
1
answer
399
views
monotone parabolic systems, convex variational structure and Legendre transform
The context:
for my research I am currently looking at parabolic systems of the type
$$
\left\{
\begin{array}{ll}
\partial_t b(u)-\Delta u=0 \qquad & (t,x)\in \mathbb{R}^+\times\Omega\\
u=0 & ...
- 5,380