Yazar "Goldstein, Jerome A." seçeneğine göre listele

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    Fast diffusion equations on riemannian manifolds
    (KHAYYAM PUBL CO INC, 2020) Bakim, Sumeyye; Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Kombe, Ismail
    In the present paper, we first study the nonexistence of positive solutions of the following nonlinear parabolic problem {partial derivative u/partial derivative t = Delta g(u(m)) + V(x)u(m) + lambda u(q) in Omega x (0, T), u(x, 0) = u(0)(x) >= 0 in Omega, u(x, t) = 0 on partial derivative Omega x (0, T). Here, Omega is a bounded domain with smooth boundary in a complete non-compact Riemannian manifold M, 0 < m < 1, V is an element of L-loc(1)(Omega), q > 0 and A E R. Next, we prove some Hardy and Leray type inequalities with remainders on a Riemannian Manifold M. Furthermore, we obtain explicit (sometimes optimal) constants for these inequalities and present several nonexistence results with help of Hardy and Leray type inequalities on the hyperbolic space H-n.
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    A general approach to weighted Rellich type inequalities on Carnot groups
    (Springer-Verlag Wien, 2018) Goldstein, Jerome A.; Kömbe, İsmail; Yener, Abdullah
    We give a simple sufficient criterion on a pair of nonnegative weight functions a and b on a Carnot group G, so that the following general weighted Lp Rellich type inequality?Ga|?Gu|pdx??Gb|u|pdxholds for every u?C0?(G) and p> 1. It is worthwhile to notice that our method easily derives previously known weighted Rellich type inequalities with a sharp constant in a more adequate fashion and also enables us to obtain new ones. We also present a sharp Lp Rellich type inequality that connects first to second order derivatives and some new two-weight Rellich type inequalities with remainders on bounded domains ? in G via a differential inequality and the improved two-weight Hardy inequality in Goldstein et al. (Discret Contin Dyn Syst 37:2009–2021, 2017). © 2017, Springer-Verlag Wien.
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    Non-existence results for p-laplacian parabolic problems on the heisenberg group Hn
    (American Institute of Mathematical Sciences, 2023) Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Kombe, Ismail
    Let Hn = Cn R be the 2n+1-dimensional Heisenberg group and be a bounded domain with smooth boundary @ in Hn. This paper deals with the nonexistence of positive solutions to the problem(Formula Presented) where Lu is the subelliptic p-Laplacian operator on the Heisenberg group Hn, p > 1, 2 R, s > 0, V 2 L1 loc(), 2 R and q > 0. We also demonstrate several applications of our main result using concrete potentials with sharp constants derived from Hardy and Leray type inequalities.
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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.
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    Scaling and instantaneous blow up
    (Taylor and Francis Ltd., 2024) Goldstein, Gisèle Ruiz; Goldstein, Jerome A.; Kömbe, İsmail; Rhandi, Abdelaziz
    The main result is a simple proof of the Baras-Goldstein (1984) instantaneous blow up result for the heat equation with the inverse square potential. The proof relies heavily, indeed mainly, on scaling. Remarks are also given concerning the case when the underlying space ?N is replaced by the Heisenberg group ?N.