Email this article An integro-differential inequality related to the smallest positive eigenvalue of p(x)-Laplacian Dirichlet problem
Abstract
Keywords
Mathematics Subject Classification (2010)
References
Ashraf, Usman, and Vakhtang Kokilashvili, and Alexander Meskhi. "Weight characterization of the trace inequality for the generalized Riemann-Liouville transform in Lp(x) spaces." Math. Inequal. Appl. 13, no. 1 (2010): 63-81.
Bodzioch, Mariusz, and Mikhail Borsuk. "On the degenerate oblique derivative problem for elliptic second-order equation in a domain with boundary conical point." Complex Var. Elliptic Equ. 59, no. 3 (2014): 324-354.
Borsuk, Mikhail, and Vladimir Kondratiev. "Elliptic boundary value problems of second order in piecewise smooth domains." Vol 69 of North-Holland Mathematical Library. Amsterdam: Elsevier Science B.V., 2006.
Borsuk, Mikhail V., and Damian Wisniewski. "Boundary value problems for quasilinear elliptic second order equations in unbounded cone-like domains." Cent. Eur. J. Math. 10, no. 6 (2012): 2051-2072.
Chen, Yunmei, and Stacey Levine, and Murali Rao. "Variable exponent, linear growth functionals in image processing." SIAM J. Appl. Math. 66 (2006): 1383-1406.
Diening, Lars. "Theorical and numerical results for electrorheological fluids." Ph.D. thesis. University of Freiburg, 2002.
Diening, Lars, and Petteri Harjulehto, and Peter Hästö, and Michael Ružicka. "Lebesgue and Sobolev spaces with variable exponents." Lecture Notes in Mathematics 2017. Heidelberg: Springer, 2011.
Fan, Xianling. "Eigenvalues of the p(x)-Laplacian Neumann problems." Nonlinear Anal. 67, no. 10 (2007): 2982–2992.
Fan, Xianling, and Qihu Zhang, and Dun Zhao. "Eigenvalues of p(x)-Laplacian Dirichlet problem." J. Math. Anal. Appl. 302, no. 2 (2005): 306-317.
Fan, Xianling, and Dun Zhao. "On the spaces Lp(x)(Ω) and Wm,p(x)(Ω)." J. Math.Anal. Appl. 263, no. 2 (2001): 424-446.
Guven, Ali, and Daniyal M. Israfilov. "Trigonometric approximation in generalized Lebesgue spaces Lp(x)." J. Math. Inequal. 4, no. 2 (2010): 285-299.
Harman, Aziz. "On necessary and sufficient conditions for variable exponent Hardy inequality." Math. Inequal. Appl. 17, no. 1 (2014): 113-119.
Kovácik, Ondrej, and Jirí Rákosník. "On spaces Lp(x) and Wk,p(x)." Czechoslovak Math. J. 41(116), no. 4, (1991): 592-618.
Liu, Wulong and Peihao Zhao. "Existence of positive solutions for p(x)-Laplacian equations in unbounded domains." Nonlinear Anal. 69, no. 10 (2008): 3358-3371.
Mihailescu, Mihai, and Vicentiu Radulescu, and Denisa Stancu-Dumitru. "A Caffarelli-Kohn-Nirenberg-type inequality with variable exponent and applications to PDEs." Complex Var. Elliptic Equ. 56, no. 7-9, (2011): 659-669.
Ružicka, Michael. "Electrorheological fluids: modeling and mathematical theory." Lecture Notes in Mathematics 1748. Berlin: Springer-Verlag, 2000.
Yao, Fengping. "Local gradient estimates for the p(x)-Laplacian elliptic equations." Math. Inequal. Appl. 17, no. 1 (2014): 259–268.
Wisniewski, Damian. "Boundary value problems for a second-order elliptic equation in unbounded domains." Ann. Univ. Paedagog. Crac. Stud. Math. 9 (2010): 87-122.
Download statistics: 1749
This article by Damian Wiśniewski, Mariusz Bodzioch is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.
Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more
The Journal is indexed in:
AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019