On the Best Constant Problem for a Class of Mixed-Norm Hardy Inequalities
نویسندگان
چکیده
Abstract In this paper, we obtain the best constant and equality condition for a class of mixed-norm Hardy inequalities when weight is power function. By building solving corresponding Euler equation, look optimal One main ingredients to introduce two key auxiliary functions so that equalities are derived.
منابع مشابه
The Effect of Curvature on the Best Constant in the Hardy-sobolev Inequalities
when 0 < s < 2, 2 := 2∗(s) = 2(n−s) n−2 , and when 0 is on the boundary ∂Ω. This question is closely related to the geometry of ∂Ω, as we extend here the main result obtained in [15] by proving that at least in dimension n ≥ 4, the negativity of the mean curvature of ∂Ω at 0 is sufficient to ensure the attainability of μs(Ω). Key ingredients in our proof are the identification of symmetries enj...
متن کاملreflections on taught courses of the iranian ma program in english translation: a mixed-methods study
the issue of curriculum and syllabus evaluation and revision has been in center of attention right from when curriculum came into attention of educational institutions. thus everywhere in the world in educational institutions curricula and syllabi are evaluated and revised based on the goals, the needs, existing content, etc.. in iran any curriculum is designed in a committee of specialists and...
The Best Constant in a Fractional Hardy Inequality
We prove an optimal Hardy inequality for the fractional Laplacian on the half-space. 1. Main result and discussion Let 0 < α < 2 and d = 1, 2, . . .. The purpose of this note is to prove the following Hardy-type inequality in the half-space D = {x = (x1, . . . , xd) ∈ R : xd > 0}. Theorem 1. For every u ∈ Cc(D), (1) 1 2 ∫
متن کاملthe algorithm for solving the inverse numerical range problem
برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2021
ISSN: ['1572-9036', '0167-8019']
DOI: https://doi.org/10.1007/s10440-021-00398-2