Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stefan problem and free targets of optimal Brownian martingale
  transport   We formulate and solve a free target optimal Brownian stopping problem from a
given distribution while the target distribution is free and is conditioned to
satisfy a given density height constraint. The solutions to this optimization
problem then generate solutions to the Stefan problem for both supercooled
fluid freezing $(St_1)$ and ice melting $(St_2)$, depending on the type of cost
for optimality. The freezing $(St_1)$ case has not been well understood in the
literature beyond one dimension, while our result gives a well-posedness of
weak solution in general dimensions, with naturally chosen initial data. The
cost is a Lagrangian type integral along path, where the Lagrangian function
satisfies strict time monotonicity, increasing (Type (I) or decreasing (Type
(II)). Type (I) case corresponds to the freezing fluid while type (II) to the
melting ice. The optimal stopping time is characterized by the hitting time to
a certain monotone barrier set in the space-time, while the optimal target
distribution saturates the density constraint. The barrier sets are determined
by the type of the cost and the initial distribution, and give the space-time
free boundaries of the flow for the Stefan problems $(St_1)$, $(St_2)$. The
free target optimization problem exhibits monotonicity, from which a remarkable
universality follows in the sense that the optimal target distribution is
independent of the cost or its type. This gives a new connection between the
freezing and melting Stefan problems.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom