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Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities
(American Mathematical Society, 2021) Goldstein, Gisele Ruiz; Goldstein, Jerome Arthur; Kömbe, İsmail; Balekoğlu Tellioğlu, Reyhan
We are primarily concerned with the absence of positive solutions of the following problem, {partial derivative u/partial derivative t = Delta (u(m)) + V (x) u(m) + lambda u(q) in Omega x (0, T), u(x, 0) = u(0)(x) >= 0 in Omega, {partial derivative u/partial derivative v = beta(x)u on partial derivative Omega x (0, T), where 0 < m < 1, V is an element of L-loc(1) (Omega), beta is an element of L-loc(1)(partial derivative Omega), lambda is an element of R, q > 0, Omega subset of R-N is a bounded open subset of R-N with smooth boundary partial derivative Omega, and partial derivative u/partial derivative v is the outer normal derivative of u on partial derivative Omega. Moreover, we also present some new sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation of our interest.