All Questions
Tagged with wasserstein partial-differential-equations
3
questions
0
votes
0
answers
21
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Regularity of Kantorovich potentials for general cost function
I know De Philippis and Figalli have a paper studying the regularity of the Kantorovich potential. In Theorem 3.3, the authors show that the potential is $C^{k+2, \beta}$ if the density functions of ...
- 11
5
votes
1
answer
130
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Advection reaction equation is solved by projection of solution of continuity equation
Suppose an absolutely continuous curve $\mu \colon (0, \infty) \to P_2(\Omega)$, where $P_2$ is the Wasserstein-2-space, fulfils the continuity equation
$$ \label{eq:CE} \tag{CE}
\partial_t \mu_t = \...
- 4,878
3
votes
1
answer
148
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Will $L^1\log L^1$ bound gives strong $L^1$ convergence?
I am trying to prove this statement: given a sequence $\{f_n | f_n > 0, c_1 \leq \int_{\Omega} f_n \log{f_n} \leq c_2 \}$, here $\Omega$ is a bounded domain; can we prove the $L^1$ strong ...
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