Regularity of weak solutions and supersolutions to the porous medium equation

الأصل · EN

We study the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish the equivalence of the conditions uᵐ ∈ L² loc(0,T;H¹ loc(Ω)) and um+12 ∈ L² loc(0,T;H¹ loc(Ω)) in the definition of weak solutions. Our proof is based on approximation by solutions to obstacle problems.