In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.
In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.
In this paper, we prove some inequalities satisfied by the modified degenerate gamma function which was recently introduced. The tools employed include Holder’s inequality, mean value theorem, Hermite–Hadamard’s inequality, and Young’s inequality. By some parameter variations, the established results reduce to the corresponding results for the classical gamma function.
In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.
In this article, we present extensions of some well-known inequalities such as Young's inequality and Qi's inequality on fractional calculus of time scales. To find generalizations of such types of dynamic inequalities, we apply the time scale Riemann-Liouville type fractional integrals. We investigate dynamic inequalities on delta calculus and their symmetric nabla results. The theory of time scales is utilized to combine versions in one comprehensive form. The calculus of time scales unifies and extends some continuous forms and their discrete and quantum inequalities. By applying the calculus of time scales, results can be generated in more general form. This hybrid theory is also extensively practiced on dynamic inequalities.
By applying the classical Holder's inequality, Young's inequality, Minkowski's inequality and some other analytical tools, we establish some inequalities involving the Chaudhry-Zubair extension of the gamma function. The established results serve as generalizations of some known results in the literature.
Hölder regularity for degenerate parabolic equations with variable exponents
