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Creators/Authors contains: "Cruz-Uribe, David"

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  1. ; ; ; (, Analysis and Mathematical Physics)
    Free, publicly-accessible full text available June 1, 2026
  2. ; ; (, Advances in Calculus of Variations)
    Abstract In this paper we study the degenerate parabolicp-Laplacian, ∂ t ⁡ u - v - 1 ⁢ div ⁡ ( | Q ⁢ ∇ ⁡ u | p - 2 ⁢ Q ⁢ ∇ ⁡ u ) = 0 {\partial_{t}u-v^{-1}\operatorname{div}(|\sqrt{Q}\nabla u|^{p-2}Q\nabla u)=0},where the degeneracy is controlled by a matrixQand a weightv.With mild integrability assumptions onQandv, we prove theexistence and uniqueness of solutions on any interval [ 0 , T ] {[0,T]}. If we further assumethe existence of a degenerate Sobolev inequality with gain, thedegeneracy again controlled byvandQ, then we can prove bothfinite time extinction and ultracontractive bounds. Moreover, weshow that there is equivalence between the existence ofultracontractive bounds and the weighted Sobolev inequality. 
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    Free, publicly-accessible full text available April 29, 2026