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

Gradient Flow Solutions For Porous Medium Equations with Nonlocal L\'{e}vy-type Pressure