A degenerate elliptic operator with unbounded diffusion coefficients

Giorgio Metafune; Chiara Spina

doi:10.4171/rlm/670

JournalsrlmVol. 25, No. 2pp. 109–140

A degenerate elliptic operator with unbounded diffusion coefficients

Giorgio Metafune
Università del Salento, Lecce, Italy
Chiara Spina
Università del Salento, Lecce, Italy

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Abstract

We prove that, for $N \geq 3$ , the operator $L = ∣ x ∣^{α} Δ$ generates an analytic semigroup in $L^{p} (R^{N})$ if $α = 2$ and $1 < p < \infty$ or $α < 2$ and $\frac{N}{N - α} < p < \infty$ or $α > 2$ and $\frac{N}{N - 2} < p < \infty$ . The above bounds are shown to be sharp.

Cite this article

Giorgio Metafune, Chiara Spina, A degenerate elliptic operator with unbounded diffusion coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 2, pp. 109–140

DOI 10.4171/RLM/670