共查询到20条相似文献,搜索用时 31 毫秒
1.
Pei‐Yong Wang 《纯数学与应用数学通讯》2000,53(7):799-810
In this paper, we study an extension of a C1,α regularity theory developed by L. Caffarelli in [2] to some fully nonlinear elliptic equations of second order. In fact, we investigate a two‐phase free boundary problem in which a fully nonlinear elliptic equation of second order is verified by the solution in the positive and the negative domains. Assuming the free boundary is locally a Lipschitz graph, we have established the C1,α regularity of the free boundary. © 2000 John Wiley & Sons, Inc. 相似文献
2.
In this paper we solve a boundary value problem in a two-dimensional domain O for a system of equations of Fluid-Poisson type, that is, a viscous approximation to a potential equation for the velocity coupled with an ordinary differential equation along the streamlines for the density and a Poisson equation for the electric field. A particular case of this system is a viscous approximation of transonic flow models. The general case is a model for semiconductors. We show existence of a density ρ, velocity potential φ, and electric potential Φ in the bounded domain O that are C1,α(O¯), C2,α(O¯), and W2,α(O¯) functions, respectively, such that ρ, φ, Φ, the speed |Δφ|, and the electric field E = ΔΦ are uniformly bounded in the viscous parameter. This is a necessary step in the existing programs in order to show existence of a solution for the transonic flow problem. © 1996 John Wiley & Sons, Inc. 相似文献
3.
We establish the existence and stability of multidimensional transonic shocks (hyperbolic‐elliptic shocks) for the Euler equations for steady compressible potential fluids in infinite cylinders. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for velocity, can be written as a second order nonlinear equation of mixed elliptic‐hyperbolic type for the velocity potential. The transonic shock problem in an infinite cylinder can be formulated into the following free boundary problem: The free boundary is the location of the multidimensional transonic shock which divides two regions of C1,α flow in the infinite cylinder, and the equation is hyperbolic in the upstream region where the C1,α perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem in unbounded domains. Our results indicate that there exists a solution of the free boundary problem such that the equation is always elliptic in the unbounded downstream region, the uniform velocity state at infinity in the downstream direction is uniquely determined by the given hyperbolic phase, and the free boundary is C1,α, provided that the hyperbolic phase is close in C1,α to a uniform flow. We further prove that, if the steady perturbation of the hyperbolic phase is C2,α, the free boundary is C2,α and stable under the steady perturbation. © 2003 Wiley Periodicals Inc. 相似文献
4.
Werner Varnhorn 《PAMM》2014,14(1):741-742
With methods of hydrodynamical potential theory we construct a solution of the Stokes resolvent equations in 2d exterior domains with C1,α-boundaries, 0 < α ≤ 1. The resulting system of boundary integral equations is uniquely solvable for small resolvent parameter λ and allows the limiting procedure λ → 0. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Emmanouil Milakis 《偏微分方程通讯》2013,38(8):1227-1252
We obtain local C α, C 1,α, and C 2,α regularity results up to the boundary for viscosity solutions of fully nonlinear uniformly elliptic second order equations with Neumann boundary conditions. 相似文献
6.
V. Kirvalidze 《Mathematical Methods in the Applied Sciences》1997,20(15):1257-1269
The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and Cα-smoothness (with α<1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
7.
Lars Diening 《Mathematische Nachrichten》2004,268(1):31-43
We study the Riesz potentials Iαf on the generalized Lebesgue spaces Lp(·)(?d), where 0 < α < d and Iαf(x) ? ∫equation/tex2gif-inf-3.gif |f(y)| |x – y|α – d dy. Under the assumptions that p locally satisfies |p(x) – p(x)| ≤ C/(– ln |x – y|) and is constant outside some large ball, we prove that Iα : Lp(·)(?d) → Lp?(·)(?d), where . If p is given only on a bounded domain Ω with Lipschitz boundary we show how to extend p to on ?d such that there exists a bounded linear extension operator ? : W1,p(·)(Ω) ? (?d), while the bounds and the continuity condition of p are preserved. As an application of Riesz potentials we prove the optimal Sobolev embeddings Wk,p(·)(?d) ?Lp*(·)(Rd) with and W1,p(·)(Ω) ? Lp*(·)(Ω) for k = 1. We show compactness of the embeddings W1,p(·)(Ω) ? Lq(·)(Ω), whenever q(x) ≤ p*(x) – ε for some ε > 0. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
In the present paper we prove Cα-estimates for ∇ u using components of boundary values of u , div u , curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G¯⊂ℝ3, meanwhile the cohomology group will be defined with regard to ℝ3−G. Our inequalities turn out to be a priori estimates concerning well-known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
9.
Grace Piper 《Mathematical Logic Quarterly》2009,55(5):562-568
We develop the theory of Cκ, λi, a strongly normal filter over ??κ λ for Mahlo κ. We prove a minimality result, showing that any strongly normal filter containing {x ∈ ??κ λ: |x | = |x ∩ κ | and |x | is inaccessible} also contains Cκ, λi. We also show that functions can be used to obtain a basis for Cκ, λi (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Basim Samir 《代数通讯》2013,41(6):2425-2436
Let α be an ordinal and κ be a cardinal, both infinite, such that κ ≤ |α|. For τ ∈αα, let sup(τ) = {i ∈ α: τ(i) ≠ i}. Let G κ = {τ ∈αα: |sup(τ)| < κ}. We consider variants of polyadic equality algebras by taking cylindrifications on Γ ? α, |Γ| < κ and substitutions restricted to G κ. Such algebras are also enriched with generalized diagonal elements. We show that for any variety V containing the class of representable algebas and satisfying a finite schema of equations, V fails to have the amalgamation property. In particular, many varieties of Halmos’ quasi-polyadic equality algebras and Lucas’ extended cylindric algebras (including that of the representable algebras) fail to have the amalgamation property. 相似文献
11.
We study the regularity and behavior at the origin of solutions to the two‐dimensional degenerate Monge‐Ampère equation det D2u = |x|α with α > ?2. We show that when α > 0, solutions admit only two possible behaviors near the origin, radial and nonradial, which in turn implies C2, δ‐regularity. We also show that the radial behavior is unstable. For α < 0 we prove that solutions admit only the radial behavior near the origin. © 2008 Wiley Periodicals, Inc. 相似文献
12.
In the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation ?Δu + g(x, u) = 0 in a smooth domain Ω ? ?N, for a general class of positive nonlinearities. This class includes every space independent, monotone increasing g which satisfies the Keller‐Osserman condition as well as degenerate nonlinearities gα,q of the form gα,q (x, u) = d(x, ?Ω)α |u|q?1 u, with α > ?2 and q > 1. The boundary trace is given by a positive regular Borel measure which may blow up on compact sets. In the second part we concentrate on the family of nonlinearities {gα,q}, determine the critical value of the exponent q (for fixed α > ?2) and discuss (a) positive solutions with an isolated singularity, for subcritical nonlinearities and (b) the boundary value problem for ?Δu + gα,q (x, u) = 0 with boundary data given by a positive regular Borel measure (possibly unbounded). We show that, in the subcritical case, the problem possesses a unique solution for every such measure. © 2003 Wiley Periodicals, Inc. 相似文献
13.
Tim Steger 《Milan Journal of Mathematics》1997,67(1):77-85
Let Γ be a free nonabelian group on finitely many generators. Let Ω be the boundary of Γ, letC(Ω) be theC *-algebra of continuous functions on Ω, and let λ be the natural action of Γ onC(Ω). Aboundary representation is a representation of the crossed productC *-algebra Γ×λ C(Ω). Given a unitary representation π of Γ onH, aboundary realization of π is an isometric Γ-inclusion ofH into the space of a boundary representation whose image is cyclic for that boundary representation. If the Γ-inclusion is bijective, we call, the realizationperfect. We prove below that if π admits an imperfect boundary realization, then there exists a nonzero vectorv 0∈H satisfying $$\sum\limits_{|x| = n} {|\left\langle {v,\pi (x)v_0 } \right\rangle |^2 \leqslant |v|^2 } for each v \in {\mathcal{H}} (GVB)$$ If π is irreducible and weakly contained in the regular representation, and if no suchv 0 exists, it follows that π satisfiesmonotony: up to equivalence, there exists exactly one realization of π, and that realization is perfect. 相似文献
14.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(12):1377-1380
We prove that the solution of the oblique derivative parabolic problem in a noncylindrical domain ΩT belongs to the anisotropic Holder space C2+α, 1+α/2(gwT) 0 < α < 1, even if the nonsmooth “lateral boundary” of ΩT is only of class C1+α, (1+α)/2). As a corollary, we also obtain an a priori estimate in the Hölder space C2+α(Ω0) for a solution of the oblique derivative elliptic problem in a domain Ω0 whose boundary belongs only to the classe C1+α. 相似文献
15.
Cheng He 《数学学报(英文版)》1999,15(2):153-164
By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability,
we establish the global existence theorem of strong solutions for Navier-Stokes equatios in arbitrary three dimensional domain
with uniformlyC
3 boundary, under the assumption that |a|
L
2(Θ) + |f|
L
1(0,∞;L
2(Θ)) or |∇a|
L
2(Θ) + |f|
L
2(0,∞;L
2(Θ)) small or viscosityv large. Herea is a given initial velocity andf is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary
conditions is also discussed.
This work is supported by foundation of Institute of Mathematics, Academia Sinica 相似文献
16.
Jacek Gulgowski 《Mathematische Nachrichten》2005,278(4):401-408
In this paper we deal with boundary value problems where l : C1([a, b], ?k) → ?k × ?k is continuous, μ ≤ 0 and φ is a Caratheodory map. We define the class S of maps l, for which a global bifurcation theorem holds for the problem (+), with φ(t, x, y, λ) = λ(|x1|, …, |xk|) + o(|x| + |y|). We show that the class S contains Sturm‐Liouville boundary conditions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
《代数通讯》2013,41(7):3519-3527
Abstract Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K α G-modules and the set of irreducible K α C G (A)-modules. 相似文献
18.
Tatsien Li 《Mathematical Methods in the Applied Sciences》2006,29(13):1543-1553
By means of a direct and constructive method based on the theory of semi‐global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
19.
Matthias Büger 《Mathematische Nachrichten》2001,222(1):31-78
We examine the autonomous reaction–diffusion system with Dirichlet boundary conditions on (0, 1), where α, β are real, α > 0, and g is C1 and satisfies some conditions which we need in order to prove the existence of solutions. We construct a solution of (RD) for every initial value in L2((0, 1)) × L2((0, 1)), we show that this solution is uniquely determined and that the solution has C∞–smooth representatives for all positive t. We determine the long time behaviour of each solution. In particular, we show that each solution of (RD) tends either to the zero solution or to a periodic orbit. We construct all periodic orbits and show that their number is always finite. It turns out that the global attractor is a finite union of subsets of L2 × L2, which are finite–dimensional manifolds, and the dynamics in these sets can be described completely. 相似文献
20.
Prof.Dr. Wolf von Wahl 《manuscripta mathematica》1974,13(2):187-206
This paper deals with the question of the existence of classical solutions for the equations $$\frac{{\partial ^{2} u}{\partial t^{2} }} + \sum_{\begin{subarray}{l} |\alpha| \leqslant m \\ | \beta | \leqslant m \end{subarray}} D^{\alpha} (A_{\alpha \beta } (x,t) D^{\beta} u) = f (t,x,u)$$ on [0,T] × G. G is a bounded or unbounded domain; the differential operator in the space variables is elliptic; the initial values of u are prescribed and Dαu (t,x) vanishes for (t,x) ∈ [0,T] × ?G, |α|≤ m?1. First we develop a method for solving regularly linear wave equations. In contrast to the usual compatibility conditions, our method requires less differentiability in t but imposes some boundary conditions on f(t). It allows some applications to nonlinear problems which will be treated in the second part of this paper and which e.g. enable us to solve ?2 u/?t2?A(t)u+u3=f. 相似文献