排序方式: 共有36条查询结果,搜索用时 46 毫秒
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An improved Hardy-Sobolev inequality and its application 总被引:4,自引:0,他引:4
Adimurthi Nirmalendu Chaudhuri Mythily Ramaswamy 《Proceedings of the American Mathematical Society》2002,130(2):489-505
For , a bounded domain, and for , we improve the Hardy-Sobolev inequality by adding a term with a singular weight of the type . We show that this weight function is optimal in the sense that the inequality fails for any other weight function more singular than this one. Moreover, we show that a series of finite terms can be added to improve the Hardy-Sobolev inequality, which answers a question of Brezis-Vazquez. Finally, we use this result to analyze the behaviour of the first eigenvalue of the operator as increases to for .
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Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem 总被引:1,自引:0,他引:1
In this paper we deal with three types of problems concerning the Hardy-Rellich's embedding for a bi-Laplacian operator. First we obtain the Hardy-Rellich inequalities in the critical dimension n=4. Then we derive a maximum principle for fourth order operators with singular terms. Then we study the existence, non-existence, simplicity and asymptotic behavior of the first eigenvalue of the Hardy-Rellich operator under various assumptions on the perturbation q. 相似文献
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An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r
−b
for functions in
\mathbbRn{\mathbb{R}^n}. The exact Hardy constant c
b
= c
b
(n) is found and generalized minimizers are given. The constant c
b
vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in
\mathbbR2{\mathbb{R}^2}. Analogous inequalities are proved in the case c
b
= 0 under constraints and, with error terms, for a bounded domain. 相似文献
5.
Adimurthi João Marcos do Ó Kyril Tintarev 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):467-477
The paper studies quasilinear elliptic problems in the Sobolev spaces W 1,p (Ω), ${\Omega\subset{\mathbb R}^N}The paper studies quasilinear elliptic problems in the Sobolev spaces W
1,p
(Ω),
W ì \mathbb RN{\Omega\subset{\mathbb R}^N} , with p = N, that is, the case of Pohozhaev–Trudinger–Moser inequality. Similarly to the case p < N where the loss of compactness in
W1,p(\mathbb RN){W^{1,p}({\mathbb R}^N)} occurs due to dilation operators u ?t(N-p)/pu(tx){u {\mapsto}t^{(N-p)/p}u(tx)} , t > 0, and can be accounted for in decompositions of the type of Struwe’s “global compactness” and its later refinements, this
paper presents a previously unknown group of isometric operators that leads to loss of compactness in W01,N{W_0^{1,N}} over a ball in
\mathbb RN{{\mathbb R}^N} . We give a one-parameter scale of Hardy–Sobolev functionals, a “p = N”-counterpart of the H?lder interpolation scale, for p > N, between the Hardy functional
ò\frac|u|p|x|p dx{\int \frac{|u|^p}{|x|^p}\,{\rm d}x} and the Sobolev functional ò|u|pN/(N-mp) dx{\int |u|^{pN/(N-mp)} \,{\rm d}x} . Like in the case p < N, these functionals are invariant with respect to the dilation operators above, and the respective concentration-compactness
argument yields existence of minimizers for W
1,N
-norms under Hardy–Sobolev constraints. 相似文献
6.
Adimurthi Maria J. Esteban 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):243-263
In this paper we prove new Hardy-like inequalities with optimal potential singularities for functions in W1,p(Ω), where Ω is either bounded or the whole space
and also some extensions to arbitrary Riemannian manifolds. We also study the spectrum of perturbed Schr?dinger operators
for perturbations which are just below the optimality threshold for the corresponding Hardy inequality. 相似文献
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We study the continuous as well as the discontinuous solutions of Hamilton-Jacobi equationu
t +H(u,Du) =g in ℝ
n
x ℝ+ withu(x, 0) =u
0(x). The HamiltonianH(s,p) is assumed to be convex and positively homogeneous of degree one inp for eachs in ℝ. IfH is non increasing ins, in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous
viscosity solutions. 相似文献
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Communicated by J. Serrin 相似文献
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