We define a homogeneous De Giorgi class of order p >= 2 that contains the solutions of two evolution equations of elliptic-parabolic and forward-backward parabolic type like p(x, t)u(t)+ Au = 0 and (p(x, t)u)(t)+ Au = 0, where p, for simplicity, takes values in the set {-1, 0, 1}, and A a suitable monotone operator. For functions belonging to this class, we prove an unusual local boundedness result.
LOCAL BOUNDEDNESS FOR FORWARD-BACKWARD PARABOLIC DE GIORGI CLASSES WITHOUT ASSUMING HIGHER REGULARITY
Paronetto, F
2022
Abstract
We define a homogeneous De Giorgi class of order p >= 2 that contains the solutions of two evolution equations of elliptic-parabolic and forward-backward parabolic type like p(x, t)u(t)+ Au = 0 and (p(x, t)u)(t)+ Au = 0, where p, for simplicity, takes values in the set {-1, 0, 1}, and A a suitable monotone operator. For functions belonging to this class, we prove an unusual local boundedness result.File in questo prodotto:
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