Displaying similar documents to “2-dimensional primal domain decomposition theory in detail”

On some L p -estimates for solutions of elliptic equations in unbounded domains

Sara Monsurrò, Maria Transirico (2015)

Mathematica Bohemica

Similarity:

In this review article we present an overview on some a priori estimates in L p , p > 1 , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two L p -bounds, p > 2 , for...

Finite element variational crimes in the case of semiregular elements

Alexander Ženíšek (1996)

Applications of Mathematics

Similarity:

The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain Ω whose boundary Ω is formed by two circles Γ 1 , Γ 2 with the same center S 0 and radii R 1 , R 2 = R 1 + ϱ , where ϱ R 1 . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for u = 0 are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus...

On sum-product representations in q

Mei-Chu Chang (2006)

Journal of the European Mathematical Society

Similarity:

The purpose of this paper is to investigate efficient representations of the residue classes modulo q , by performing sum and product set operations starting from a given subset A of q . We consider the case of very small sets A and composite q for which not much seemed known (nontrivial results were recently obtained when q is prime or when log | A | log q ). Roughly speaking we show that all residue classes are obtained from a k -fold sum of an r -fold product set of A , where r log q and log k log q , provided the...

A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem

Caroline Sweezy (2007)

Annales Polonici Mathematici

Similarity:

Let L be a strictly elliptic second order operator on a bounded domain Ω ⊂ ℝⁿ. Let u be a solution to L u = d i v f in Ω, u = 0 on ∂Ω. Sufficient conditions on two measures, μ and ν defined on Ω, are established which imply that the L q ( Ω , d μ ) norm of |∇u| is dominated by the L p ( Ω , d v ) norms of d i v f and | f | . If we replace |∇u| by a local Hölder norm of u, the conditions on μ and ν can be significantly weaker.

Dimension of weakly expanding points for quadratic maps

Samuel Senti (2003)

Bulletin de la Société Mathématique de France

Similarity:

For the real quadratic map P a ( x ) = x 2 + a and a given ϵ > 0 a point x has good expansion properties if any interval containing x also contains a neighborhood  J of x with P a n | J univalent, with bounded distortion and B ( 0 , ϵ ) P a n ( J ) for some n . The ϵ -weakly expanding set is the set of points which do not have good expansion properties. Let α denote the negative fixed point and M the first return time of the critical orbit to [ α , - α ] . We show there is a set of parameters with positive Lebesgue measure for which the Hausdorff...

A quantitative aspect of non-unique factorizations: the Narkiewicz constants III

Weidong Gao, Jiangtao Peng, Qinghai Zhong (2013)

Acta Arithmetica

Similarity:

Let K be an algebraic number field with non-trivial class group G and K be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let F k ( x ) denote the number of non-zero principal ideals a K with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that F k ( x ) behaves for x → ∞ asymptotically like x ( l o g x ) 1 - 1 / | G | ( l o g l o g x ) k ( G ) . We prove, among other results, that ( C n C n ) = n + n for all integers n₁,n₂ with 1 < n₁|n₂.

Poisson geometry and deformation quantization near a strictly pseudoconvex boundary

Eric Leichtnam, Xiang Tang, Alan Weinstein (2007)

Journal of the European Mathematical Society

Similarity:

Let X be a complex manifold with strongly pseudoconvex boundary M . If ψ is a defining function for M , then log ψ is plurisubharmonic on a neighborhood of M in X , and the (real) 2-form σ = i ¯ ( log ψ ) is a symplectic structure on the complement of M in a neighborhood of M in X ; it blows up along M . The Poisson structure obtained by inverting σ extends smoothly across M and determines a contact structure on M which is the same as the one induced by the complex structure. When M is compact, the Poisson structure...

Limits of log canonical thresholds

Tommaso de Fernex, Mircea Mustață (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let 𝒯 n denote the set of log canonical thresholds of pairs ( X , Y ) , with X a nonsingular variety of dimension n , and Y a nonempty closed subscheme of X . Using non-standard methods, we show that every limit of a decreasing sequence in 𝒯 n lies in 𝒯 n - 1 , proving in this setting a conjecture of Kollár. We also show that 𝒯 n is closed in 𝐑 ; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in...

When C p ( X ) is domain representable

William Fleissner, Lynne Yengulalp (2013)

Fundamenta Mathematicae

Similarity:

Let M be a metrizable group. Let G be a dense subgroup of M X . We prove that if G is domain representable, then G = M X . The following corollaries answer open questions. If X is completely regular and C p ( X ) is domain representable, then X is discrete. If X is zero-dimensional, T₂, and C p ( X , ) is subcompact, then X is discrete.

Existence and nonexistence of solutions for a quasilinear elliptic system

Qin Li, Zuodong Yang (2015)

Annales Polonici Mathematici

Similarity:

By a sub-super solution argument, we study the existence of positive solutions for the system ⎧ - Δ p u = a ( x ) F ( x , u , v ) in Ω, ⎪ - Δ q v = a ( x ) F ( x , u , v ) in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in N with smooth boundary or Ω = N . A nonexistence result is obtained for radially symmetric solutions.

Some characterizations of the class m ( Ω ) and applications

Hai Mau Le, Hong Xuan Nguyen, Hung Viet Vu (2015)

Annales Polonici Mathematici

Similarity:

We give some characterizations of the class m ( Ω ) and use them to establish a lower estimate for the log canonical threshold of plurisubharmonic functions in this class.

Curved thin domains and parabolic equations

M. Prizzi, M. Rinaldi, K. P. Rybakowski (2002)

Studia Mathematica

Similarity:

Consider the family uₜ = Δu + G(u), t > 0, x Ω ε , ν ε u = 0 , t > 0, x Ω ε , ( E ε ) of semilinear Neumann boundary value problems, where, for ε > 0 small, the set Ω ε is a thin domain in l , possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of l . If G is dissipative, then equation ( E ε ) has a global attractor ε . We identify a “limit” equation for the family ( E ε ) , prove convergence of trajectories and establish an upper semicontinuity result for the family ε as ε → 0⁺. ...

Scaling limit and cube-root fluctuations in SOS surfaces above a wall

Pietro Caputo, Eyal Lubetzky, Fabio Martinelli, Allan Sly, Fabio Lucio Toninelli (2016)

Journal of the European Mathematical Society

Similarity:

Consider the classical ( 2 + 1 ) -dimensional Solid-On-Solid model above a hard wall on an L × L box of 2 . The model describes a crystal surface by assigning a non-negative integer height η x to each site x in the box and 0 heights to its boundary. The probability of a surface configuration η is proportional to exp ( - β ( η ) ) , where β is the inverse-temperature and ( η ) sums the absolute values of height differences between neighboring sites. We give a full description of the shape of the SOS surface for low enough...

Uniform algebras and analytic multi­functions

Zbigniew Slodkowski (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Dati due elementi f e g in un'algebra uniforme A , sia G = f ( M A / f ( A ) . Nella presente Nota si danno, fra l’altro, due nuove dimostrazioni elementari del fatto che la funzione λ log max g ( f - 1 ( λ ) ) è subarmonica su G e che l’applicazione λ g ( f - 1 ( λ ) ) è analitica nel senso di Oka.

A note on representation functions with different weights

Zhenhua Qu (2016)

Colloquium Mathematicae

Similarity:

For any positive integer k and any set A of nonnegative integers, let r 1 , k ( A , n ) denote the number of solutions (a₁,a₂) of the equation n = a₁ + ka₂ with a₁,a₂ ∈ A. Let k,l ≥ 2 be two distinct integers. We prove that there exists a set A ⊆ ℕ such that both r 1 , k ( A , n ) = r 1 , k ( A , n ) and r 1 , l ( A , n ) = r 1 , l ( A , n ) hold for all n ≥ n₀ if and only if log k/log l = a/b for some odd positive integers a,b, disproving a conjecture of Yang. We also show that for any set A ⊆ ℕ satisfying r 1 , k ( A , n ) = r 1 , k ( A , n ) for all n ≥ n₀, we have r 1 , k ( A , n ) as n → ∞.

Continuous pluriharmonic boundary values

Per Åhag, Rafał Czyż (2007)

Annales Polonici Mathematici

Similarity:

Let D j be a bounded hyperconvex domain in n j and set D = D × × D s , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.

On operator-valued cosine sequences on UMD spaces

Wojciech Chojnacki (2010)

Studia Mathematica

Similarity:

A two-sided sequence ( c ) n with values in a complex unital Banach algebra is a cosine sequence if it satisfies c n + m + c n - m = 2 c c for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence ( c ) n is bounded if s u p n | | c | | < . A (bounded) group decomposition for a cosine sequence c = ( c ) n is a representation of c as c = ( b + b - n ) / 2 for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying s u p n | | b | | < , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, the...