Gradient Flow Solutions For Porous Medium Equations with Nonlocal Lévy-type Pressure

Publikation: Vorabdruck/Dokumentation/BerichtVorabdruck (Preprint)


We study a porous medium-type equation whose pressure is given by a nonlocal L\'{e}vy operator associated to a symmetric jump L\'{e}vy kernel. The class of nonlocal operators under consideration appears as a generalization of the classical fractional Laplace operator. For the class of L\'evy-operators, we construct weak solutions using a variational minimizing movement scheme. The lack of interpolation techniques is ensued by technical challenges that render our setting more challenging than the one known for fractional operators.


PublikationsstatusVeröffentlicht - 26 Nov. 2023
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  • math.AP, 35A15, 35R09, 35R11, 46E35, 47A07, 49J40, 35S10