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Rodríguez Bernal, Aníbal Cholewa, Jan W. 2023-11-17T12:30:21Z 2023-11-17T12:30:21Z 2022 Cholewa, J. W., & Rodriguez-Bernal, A. (2022). On some PDEs involving homogeneous operators. Spectral analysis, semigroups and Hardy inequalities. Journal Of Differential Equations, 315, 1-56. https://doi.org/10.1016/j.jde.2022.01.029 0022-0396 10.1016/j.jde.2022.01.029 https://hdl.handle.net/20.500.14352/88793 https://doi.org/10.1016/j.jde.2022.01.029 http://www.elsevier.com/locate/jde Motivated by the analysis of homogeneous operators and semigroups in [10], in this paper we perform an spectral analysis of homogeneous operators and give simple characterization of generators of homoge- neous semigroups and of homogeneous sectorial operators. We also analyse homogeneous perturbations of homogeneous operators and semigroups. We use these results to study some parabolic PDEs involving homogeneous operators including some fractional diffusion problems. We show a deep connection of these results with some Gagliardo–Nirenberg and Hardy type inequalities. eng http://creativecommons.org/licenses/by-nc-nd/4.0/ restricted access Attribution-NonCommercial-NoDerivatives 4.0 International On some PDEs involving homogeneous operators. Spectral analysis, semigroups and Hardy inequalities journal article