differential-equations / Kinetic theory
Does the natural trace estimate hold for kinetic energy spaces in the unrestricted Gaussian velocity model on bounded domains (Question 1.8 of Albritton, Armstrong, Mourrat and Novack)? No: for each $1 \le p < 2$ there are counterexamples on every bounded $\mathrm{C}^{1,1}$ domain in dimension $d \ge 2$. The paper also identifies the sharp boundary-regularity threshold $\mathrm{C}^{1,1/2}$ for the natural trace weight.
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the named open question is answered negatively; the paper's positive theory goes further
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Does the natural trace estimate hold for kinetic energy spaces in the unrestricted Gaussian velocity model on bounded domains (Question 1.8 of Albritton, Armstrong, Mourrat and Novack)? No: for each $1 \le p < 2$ there are counterexamples on every bounded $\mathrm{C}^{1,1}$ domain in dimension $d \ge 2$. The paper also identifies the sharp boundary-regularity threshold $\mathrm{C}^{1,1/2}$ for the natural trace weight.
the named open question is answered negatively; the paper's positive theory goes further
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