Displaying similar documents to “Solutions of nonlinear parabolic equations without growth restrictions on the data.”

The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

Jiaqing Pan (2011)

Open Mathematics

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In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.

Regularity results for a class of obstacle problems in Heisenberg groups

Francesco Bigolin (2013)

Applications of Mathematics

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We study regularity results for solutions u ∈ H W 1 , p ( Ω ) to the obstacle problem ∫ Ω 𝒜 ( x , ∇ ℍ u ) ∇ ℍ ( v - u ) d x ≥ 0 ∀ v ∈ 𝒦 ψ , u ( Ω ) such that u ≥ ψ a.e. in Ω , where 𝒦 ψ , u ( Ω ) = { v ∈ H W 1 , p ( Ω ) : v - u ∈ H W 0 1 , p ( Ω ) v ≥ ψ a.e. in Ω } , in Heisenberg groups ℍ n . In particular, we obtain weak differentiability in the T -direction and horizontal estimates of Calderon-Zygmund type, i.e. d T ψ ∈ H W loc 1 , p ( Ω ) ⇒ T u ∈ L loc p ( Ω ) , | ∇ ℍ ψ | p ∈ L loc q ( Ω ) ⇒ | ∇ ℍ u | p ∈ L loc q ( Ω ) , d where 2 < p < 4 , q > 1 .