In this paper, we study the regularity of solutions for two–dimensional Cahn–Hilliard equation with non–constant mobility. Basing on the L p type estimates and Schauder type estimates, we prove the global existence of classical solutions. [ABSTRACT FROM AUTHOR]
In this paper, we determine the general solution of the functional equation f1(2 x + y) + f2(2 x − y) = f3( x + y) + f4( x − y) + f5( x) without assuming any regularity condition on the unknown functions f1, f2, f3, f4, f5 : ℝ → ℝ. The general solution of this equation is obtained by finding the general solution of the functional equations f(2 x + y) + f(2 x − y) = g( x + y) + g( x − y) + h( x) and f(2 x + y) + f(2 x − y) = g( x + y) + g( x − y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszú. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi. [ABSTRACT FROM AUTHOR]