Yazar "Kömbe, İsmail" seçeneğine göre listele
Listeleniyor 1 - 16 / 16
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe Doubly nonlinear parabolic equations with Robin boundary conditions(Wiley, 2022) Kömbe, İsmail; Balekoğlu, Reyhan Tellioğludoubly nonlinear parabolic equations, positive solutions, Robin boundary conditionÖğe A general approach to weighted L p rellich type inequalities related to greiner operator(American Institute of Mathematical Sciences, 2019) Kömbe, İsmail; Yener, AbdullahIn this paper we exhibit some sufficient conditions that imply general weighted L p Rellich type inequality related to Greiner operator without assuming a priori symmetric hypotheses on the weights. More precisely, we prove that given two nonnegative functions a and b, if there exists a positive supersolution ? of the Greiner operator ? ? such that ? ? (a|? ? ?| p-2 ? ? ?)?b? p-1 almost everywhere in R 2n+1 ; then a and b satisfy a weighted L p Rellich type inequality. Here, p > 1 and ? ? = ? n j=1 (x 2 j +y 2 j ) is the sub-elliptic operator generated by the Greiner vector fields x j {equation presented} where (z,l)=(x,y,l)? R 2n+1 =R n ×R n ×R,|Z|={equation presented} and k ? 1. The method we use is quite practical and constructive to obtain both known and new weighted Rellich type inequalities. On the other hand, we also establish a sharp weighted L p Rellich type inequality that connects first to second order derivatives and several improved versions of two-weight L p Rellich type inequalities associated to the Greiner operator ? ? on smooth bounded domains ? in R 2n+1 . © 2019 American Institute of Mathematical Sciences. All Rights Reserved.Öğe A general approach to weighted Rellich type inequalities on Carnot groups(Springer-Verlag Wien, 2018) Goldstein, Jerome A.; Kömbe, İsmail; Yener, AbdullahWe 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.Öğe General weighted hardy type inequalities related to Baouendi-Grushin operators(Taylor and Francis Ltd., 2018) Kömbe, İsmail; Yener, AbdullahIn this paper, we derive a sufficient condition on a pair of nonnegative weight functions ? and w in ?m+k so that the general weighted Hardy type inequality with a remainder term (Formula Presented) is the sub-elliptic gradient. It is worth emphasizing here that our unifying method may be readily used to recover most of the previously known sharp weighted Hardy and Heisenberg-Pauli-Weyl type inequalities as well as to construct other new inequalities with an explicit constant. Furthermore, we also obtain new results on two-weight Lp Hardy type inequalities with remainder terms on smooth bounded domains ? in ?m+k via a non-linear partial differential inequality. © 2017 Informa UK Limited, trading as Taylor & Francis Group.Öğe Hardy and rellich type inequalities with two weight functions(Element D.O.O., 2016) Ahmetolan, Semra; Kömbe, İsmailIn the present paper we prove several sharp two-weight Hardy, Hardy-Poinca?e, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ? /? xj +2kyj |z|2k?2 ?/ ? l Yj = ? /? yj ?2kxj |z|2k?2?/ ? l, j = 1,2, ..,n where (z,y) = (x,y, l) ? R2n+1 , |z| = (|x|2 +|y|2)1/2 and k ? 1.Öğe Hardy and rellich-type inequalities with remainders for baouendi-grushin vector fields(University of Houston, 2015) Kömbe, İsmailIn this paper we study Hardy and Rellich-type inequalities and their improved versions for the Baouendi-Grushin vector fields ?? = (?x; |x|?y) where > 0, rx and ry are usual gradient operators in the variables x ? Rm and y ? Rk, respectively. We also obtain sharp constants for these inequalities. Furthermore, we prove a sharp uncertainty principle inequality for the Baouendi-Grushin vector fields. © 2015 University of Houston.Öğe Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds(2013) Kömbe, İsmail; Özaydın, MuradWe continue our previous study of improved Hardy, Rellich and uncertainty principle inequalities on a Riemannian manifold M, started in our earlier paper from 2009. In the present paper we prove new weighted Hardy-Poincaré, Rellich type inequalities as well as an improved version of our uncertainty principle inequalities on a Riemannian manifold M. In particular, we obtain sharp constants for these inequalities on the hyperbolic space ?n. © 2013 American Mathematical Society.Öğe Improved hardy and rellich type inequalities with two weight functions(Element D.O.O., 2018) Ahmetolan, Semra; Kömbe, İsmailIn this work, we obtain several improved versions of two weight Hardy and Rellich type inequalities on the sub-Riemannian manifold R 2 n+ 1 defined by the vector fields ? ? X j = ? x j + 2ky j |z| 2 k? 2 ? ? l , Y j = ? y j ? 2kx j |z| 2 k? 2 ? ? l , j = 1, 2,..., n where (z, l) = (x, y, l) ? R 2 n+ 1 , |z| = (|x| 2 + |y| 2 ) 1 / 2 and k 1 . © 2018 Element D.O.O. All rights reserved.Öğe Nonexistence results for parabolic equations involving the p-Laplacian and Hardy–Leray-type inequalities on Riemannian manifolds(Birkhauser, 2021) Goldstein, G.R.; Goldstein, J.A.; Kömbe, İsmail; Bakım, SümeyyeThe main goal of this paper is twofold. The first one is to investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation on a noncompact Riemannian manifold MÖğe On the nonexistence of positive solutions to doubly nonlinear equations for baouendi-grushin operators(2013) Kömbe, İsmailThe purpose of this paper is to study the nonexistence of positive solutions of the doubly nonlinear equation -u t = r (um-1jrujp-2ru) + V um+p-2 in (0; T); u(x; 0) = u0(x) 0 in ; u(x; t) = 0 on (0; T); where r = (rx; jxj2ry), x 2 Rd; y 2 Rk, > 0, is a metric ball in RN, V 2 L1 loc(), m 2 R, 1 < p < d + k and m + p - 2 > 0. The exponents q are found and the nonexistence results are proved for q m + p < 3.Öğe Scaling and instantaneous blow up(Taylor and Francis Ltd., 2024) Goldstein, Gisèle Ruiz; Goldstein, Jerome A.; Kömbe, İsmail; Rhandi, AbdelazizThe 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.Öğe A sharp uncertainty principle and hardy-poinca?e inequalities on sub-riemannian manifolds(Element D.O.O., 2012) Ahmetolan, Semra; Kömbe, İsmailWe prove a sharp Heisenberg uncertainty principle inequality and Hardy-Poinca?e inequality on the sub-Riemannian manifold R2n+1 = Rn ×Rn ×R defined by the vector fields: where |z| = (|x|2 +|y|2)1/2 and k1.Öğe A unified approach to weighted Hardy type inequalities on Carnot groups(Southwest Missouri State University, 2017) Goldstein, J.A.; Kömbe, İsmail; Yener, AbdullahWe find a simple sufficient criterion on a pair of nonnegative weight functions V (x) and W (x) on a Carnot group G; so that the general weighted Lp Hardy type inequality (Equation presentted) is valid for any ? ? C? 0 (G) and p > 1: It is worth noting here that our unifying method may be readily used both to recover most of the previously known weighted Hardy and Heisenberg-Pauli-Weyl type inequalities as well as to construct other new inequalities with an explicit best constant on G: We also present some new results on two-weight Lp Hardy type inequalities with remainder terms on a bounded domain ? in G via a differential inequality.Öğe Weighted Hardy and Rellich type inequalities on Riemannian manifolds(Wiley-VCH Verlag, 2016) Kömbe, İsmail; Yener, AbdullahIn this paper we present new results on two-weight Hardy, Hardy-Poincaré and Rellich type inequalities with remainder terms on a complete noncompact Riemannian Manifold M. The method we use is flexible enough to obtain more weighted Hardy type inequalities. Our results improve and include many previously known results as special cases. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.Öğe Weighted hardy type inequalities with Robin boundary conditions(American Institute of Mathematical Sciences, 2024) Kömbe, İsmail; Yener, AbdullahIn this paper, we establish a general weighted Hardy type inequality for the p?Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present some Heisenberg-Pauli-Weyl type inequalities with boundary terms on balls centred at the origin with radius R in RnÖğe Weighted rellich type inequalities related to baouendi-grushin operators(American Mathematical Society, 2017) Kömbe, İsmail; Yener, AbdullahWe find a simple sufficient criterion on a pair of nonnegative weight functions a (x, y) and b (x, y) in ?m+k so that the general weighted Lp Rellich type inequality (Formula presented) holds for all u ? C0?(?m+k). Here ?? = ?x + |x|2??y is the Baouendi-Grushin operator, ? > 0, m, k ? 1 and p > 1. It is important to point out here that our approach is constructive in the sense that it allows us to retrieve already established weighted sharp Rellich type inequalities as well as to get other new results with an explicit constant on ?m+k. We also obtain a sharp Lp Rellich type inequality that connects first to second order derivatives and several new two-weight Rellich type inequalities with remainder terms on smooth bounded domains ? in ?m+k via a nonlinear differential inequality. © 2017 American Mathematical Society.
