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Öğe First boundary value problem for cordes-type semilinear parabolic equation with discontinuous coefficients(Hindawi, 2020-06-19) Harman, Aziz; Harman, EzgiFor a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj-ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n-1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n-1,n≥2.Öğe The log-conditions for the variable exponent Hardy inequality(Hikari, 2019) Harman, AzizIn this note we discuss a logarithmic regularity condition in neighborhood of the origin on the exponent function p(x) in dependence of the weights v, ω for the variable exponent Hardy inequality v (x) 1 p(.) Zx 0 f(t)dt Lp(.)(0,l) ≤ C ω (x) 1 p(.) f (x) Lp(.)(0,l) to hold.Öğe On the dirichlet problem for semilinear eliptic equations(Yıldız Technical University, 2020) Harman, Aziz; Harman, Ezgi
