Abstract
<abstract><p>We consider a volume constraint problem for the nonlocal doubly nonlinear parabolic equation, called the nonlocal $ p $-Sobolev flow, and introduce a nonlinear intrinsic scaling, converting a prototype nonlocal doubly nonlinear parabolic equation into the nonlocal $ p $-Sobolev flow. This paper is dedicated to Giuseppe Mingione on the occasion of his 50th birthday, who is a maestro in the regularity theory of PDEs.</p></abstract>
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