F. Ben Belgacem, P.E. Jabin, Compactness for nonlinear transport
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method of compactness for scalar conservation laws work and one can for example show propagation of BV bounds on n. Unfortunately this Lipschitz bound does not hold here in general (only W 1,p , p ...
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C1 > 0 such that ν(x) ≤ C1 w(x). This implies B1,w (p, q) ⊂ L1ν (Rd ). Let (tn )n∈N be ν(x) a sequence with tn → ∞ in Rd . Also since w(x) doesn’t tend to zero as x → ∞ then ν(x) ≥ δ > 0 for x → ∞....
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