共查询到20条相似文献,搜索用时 15 毫秒
1.
Michael Bildhauer Martin Fuchs 《Calculus of Variations and Partial Differential Equations》2001,13(4):537-560
We introduce integrands of –type, which are, roughly speaking, of lower (upper) growth rate ) satisfying in addition for some . Then, if , we prove partial –regularity of local minimizers by the way including integrands f being controlled by some N–function and also integrands of anisotropic power growth. Moreover, we extend the known results up to a certain limit and
present examples which are not covered by the standard theory.
Received: 17 February 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001 相似文献
2.
M. Guidorzi 《manuscripta mathematica》2002,107(1):25-41
We prove partial regularity of minimizers of some polyconvex functionals. In particular our results include models such as
∫Ω
a(x,u)(|Du|2+| det Du|2), where a is a bounded H?lder continuous function, such that a(x,u)≥c for some positive constant c.
Received: 2 January 2001 / Revised version: 30 August 2001 相似文献
3.
We consider local minimizers a domain in , of the variational integral with integrand f of upper (lower) growth rate q (s). We show using a lemma due to Frehse and Seregin that u has H?lder continuous first derivatives provided that .
Received: 2 October 2001 / Accepted: 25 October 2001 / Published online: 28 February 2002 相似文献
4.
5.
We consider minimal energy configurations of mixtures of two materials in , where the energy includes a penalty on the length of the interface between the materials. We show that, for one of the materials,
the boundary of each component is smooth, and we prove the existence of an upper bound on the relative distances between components.
Received: 24 March 2000 / Accepted: 25 October 2001 / Published online: 29 April 2002 相似文献
6.
Pietro Celada Stefania Perrotta 《Calculus of Variations and Partial Differential Equations》2001,12(4):371-398
We consider the problem of minimizing multiple integrals of product type, i.e. where is a bounded, open set in , is a possibly nonconvex, lower semicontinuous function with p-growth at infinity for some and the boundary datum is in (or simply in if ). Assuming that the convex envelope off is affine on each connected component of the set , we prove attainment for () for every continuous, positively bounded below function g such that (i) every point is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that the class of coefficents g that yield existence to () is dense in the space of continuous, positive functions on . We present examples which show that these conditions for attainment are essentially sharp. Received April 12, 2000 / Accepted May 9, 2000 / Published online November 9, 2000 相似文献
7.
Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献
8.
The equation with boundary Dirichlet zero data is considered in a bounded domain . Under the assumption that concentrates, as , round a manifold and that f is a superlinear function, satisfying suitable growth assumptions, the existence of multiple distinct positive solutions
is proved.
Received: 19 December 2000 / Accepted: 8 May 2001 / Published online: 5 September 2002 相似文献
9.
We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisub- and quasisuperminimizers. This is done in metric spaces equipped with a doubling measure and supporting a weak (1, p)-Poincaré inequality. The metric space is not required to be complete. We also provide an example which shows that the dilation constant from the weak Poincaré inequality is essential in the condition on the balls in the Harnack inequality. This fact seems to have been overlooked in the earlier literature on nonlinear potential theory on metric spaces. 相似文献
10.
11.
J. Chabrowski M. Willem 《Calculus of Variations and Partial Differential Equations》2002,15(4):421-431
We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least
energy solutions. As a by-product we establish a Sobolev inequality with interior norm.
Received: 26 April 2000 / Accepted: 25 February 2001 / Published online: 5 September 2002 相似文献
12.
Hirofumi Osada 《Probability Theory and Related Fields》2001,119(2):275-310
We construct a family of diffusions P
α = {P
x} on the d-dimensional Sierpinski carpet F^. The parameter α ranges over d
H
< α < ∞, where d
H
= log(3
d
− 1)/log 3 is the Hausdorff dimension of the d-dimensional Sierpinski carpet F^. These diffusions P
α are reversible with invariant measures μ = μ[α]. Here, μ are Radon measures whose topological supports are equal to F^ and satisfy self-similarity in the sense that μ(3A) = 3α·μ(A) for all A∈ℬ(F^). In addition, the diffusion is self-similar and invariant under local weak translations (cell translations) of the
Sierpinski carpet. The transition density p = p(t, x, y) is locally uniformly positive and satisfies a global Gaussian upper bound. In spite of these well-behaved properties, the
diffusions are different from Barlow-Bass' Brownian motions on the Sierpinski carpet.
Received: 30 September 1999 / Revised version: 15 June 2000 / Published online: 24 January 2000 相似文献
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14.
Concerning the obstacle-problem-like equation
, where + > 0 and – > 0, we give a complete characterization of all global two-phase solutions with quadratic growth both at 0 and infinity. 相似文献
15.
We consider autonomous integrals
in the multidimensional calculus of variations, where the integrand f is a strictly W
1,p
-quasiconvex C
2-function satisfying the (p,q)-growth conditions
with exponents 1 < p ≤ q < ∞. Under these assumptions we establish an existence result for minimizers of F in provided . We prove a corresponding partial C
1,α
-regularity theorem for . This is the first regularity result for autonomous quasiconvex integrals with (p,q)-growth. 相似文献
16.
Michael Bildhauer 《manuscripta mathematica》1998,97(3):389-406
H?lder continuity up to the free boundary is proved for minimizing solutions if they meet the supporting surface in an angle
which is bounded away from zero. The problem is localized by proving the continuity of the distance function, a result which
is also true for stationary points.
Received: 14 April 1998 相似文献
17.
Optimal interior partial regularity¶for nonlinear elliptic systems: the method of A-harmonic approximation 总被引:3,自引:0,他引:3
We consider nonlinear elliptic systems of divergence type. We provide a new method for proving partial regularity for weak
solutions, based on a generalization of the technique of harmonic approximation. This method is applied to both homogeneous
and inhomogeneous systems, in the latter case with inhomogeneity obeying the natural growth condition. Our methods extend
previous partial regularity results, directly establishing the optimal H?lder exponent for the derivative of a weak solution
on its regular set. We also indicate how the technique can be applied to further simplify the proof of partial regularity
for quasilinear elliptic systems.
Received: 22 July 1999 / Revised version: 23 May 2000 相似文献
18.
Some function spaces on spaces of homogeneous type 总被引:2,自引:0,他引:2
Manfred Kronz 《manuscripta mathematica》2001,106(2):219-248
We introduce Campanato, Morrey, BMO and Sobolev-type spaces for mappings from a space of homogeneous type into a complete
metric space which possess properties comparable to their classical analogues. In particular we show integral characterizations,
the validity of the John–Nirenberg theorem, Poincarè and Sobolev inequalities, Sobolev's embedding theorem and estimates
on the pointwise behavior of Sobolev-type mappings.
Received: 4 December 2000 / Revised version: 5 July 2001 相似文献
19.
20.
John Urbas 《Mathematische Zeitschrift》2001,236(3):625-641
We derive a monotonicity formula for smooth solutions u of degenerate two dimensional Monge-Ampère equations, and use this to obtain a local H?lder gradient estimate, depending
on for some .
Received August 9, 1999; in final form December 8, 1999/ Published online December 8, 2000 相似文献