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. Lorenzi
Ultimo
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.
Settore MAT/05 - Analisi Matematica
2007
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/37222
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