In this talk, we study nonlinear drift diffusion equations with measure valued external forces, focusing on the porous medium and fast diffusion regimes By introducing a new class of energy estimates that effectively handle both measure data and drift terms, we establish the existence of nonnegative weak solutions with gradient estimates under broad conditions on the drift This is joint work with Sukjung Hwang, Kyungkeun Kang, and Hwa Kil Kim.
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