For p ∈ (1,+∞) we derive a weighted Lp estimate for the (spatial) gradient of the solution u of a degenerate parabolic differential equation. Here the underlying domain ω ⊂ Rn, n ≥ 2, is unbounded and the equation may degenerate only at infinity along some unbounded branch of ω. Our estimate is strictly related with the still-open problem of giving a concrete characterization of the interpolation space between W2,p(ω) and Lp(ω) to which the (spatial) gradient of u belongs.
Gradient estimates for solutions of parabolic differential equations degenerating at infinity / A. Favaron, A. Lorenzi. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 12:4(2007), pp. 435-460.
Gradient estimates for solutions of parabolic differential equations degenerating at infinity
A. LorenziUltimo
2007
Abstract
For p ∈ (1,+∞) we derive a weighted Lp estimate for the (spatial) gradient of the solution u of a degenerate parabolic differential equation. Here the underlying domain ω ⊂ Rn, n ≥ 2, is unbounded and the equation may degenerate only at infinity along some unbounded branch of ω. Our estimate is strictly related with the still-open problem of giving a concrete characterization of the interpolation space between W2,p(ω) and Lp(ω) to which the (spatial) gradient of u belongs.Pubblicazioni consigliate
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