Existence and uniqueness are established for solutions to the viscous conservation law with positive measure initial data when the flux satisfies a p-condition.
Beckner, Geometric proof of Nash’s inequality, IMRN 2 (1998), 67 –71
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Viscous Conservation Laws in 1d With Measure Initial Data
Existence and uniqueness are established for solutions to the viscous conservation law with positive measure initial data when the flux satisfies a p-condition.