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 N3N \ge 3, the operator L=xαΔL=|x|^\alpha\Delta generates an analytic semigroup in Lp(RN)L^{p}(\R^N) if α=2\alpha=2 and 1<p<1<p<\infty or α<2\alpha<2 and NNα<p<\frac{N}{N-\alpha}< p<\infty or α>2\alpha> 2 and NN2<p<\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