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    Nonexistence of positive solutions for nonlinear parabolic Robin problems and Hardy–Leray inequalities
    (Institute for Ionics, 2022) Goldstein, Gisèle Ruiz; Goldstein, Jerome A.; Kömbe, Ismail; Tellioğlu, Reyhan
    The purpose of this paper is twofold. First is the study of the nonexistence of positive solutions of the parabolic problem {?u?t=?pu+V(x)up-1+?uqin?×(0,T),u(x,0)=u0(x)?0in?,|?u|p-2?u??=?|u|p-2uon??×(0,T),where ? is a bounded domain in RN with smooth boundary ??, ?pu= div (| ? u| p-2? u) is the p-Laplacian of u, V?Lloc1(?), ??Lloc1(??), ?? R, the exponents p and q satisfy 1 < p< 2 , and q> 0. Then, we present some sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation we are interested in.