Regularity for elliptic pairs over $ \mathbb {C}[[] $

David Raimundo

Displaying similar documents to “Regularity for elliptic pairs over $ℂ [[]$ ”

Some Results About Holonomic $ε$ -Modules

Jan-Erik Björk (1983)

Recherche Coopérative sur Programme n°25

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Lifting $D$ -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

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We study liftings or deformations of $D$ -modules ( $D$ is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic $D$ -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given $D$ -module in positive characteristic. At the end we compare...

The correspondence between Barsotti-Tate groups and Kisin modules when $p = 2$

Tong Liu (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $K$ be a finite extension over $ℚ_{2}$ and $𝒪_{K}$ the ring of integers. We prove the equivalence of categories between the category of Kisin modules of height 1 and the category of Barsotti-Tate groups over $𝒪_{K}$ .

On extensions of families of operators

Oleg Lihvoinen (2023)

Commentationes Mathematicae Universitatis Carolinae

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The strong closure of feasible states of families of operators is studied. The results are obtained for self-adjoint operators in reflexive Banach spaces and for more concrete case - families of elliptic systems encountered in the optimal layout of $r$ materials. The results show when it is possible to parametrize the strong closure by the same type of operators. The results for systems of elliptic operators for the case when number of unknown functions $m$ is less than the dimension $n$ of...

Partially elliptic differential equations having distributions as their right members

H. Marcinkowska

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ContentsIntroduction.............................................................................................................................31. Definitions, notations and some auxiliary lemmas...................................................42. The definition of the spaces $H_{p, q; Y} (Ω, ℬ)$ ..........................................................73. Some properties of the spaces $H_{p, q; Y} (Ω, ℬ)$ ...................................................104. Some examples of the spaces $H_{p, q; Y} (Ω, ℬ)$ ....................................................155....

CF-modules over commutative rings

Ahmed Najim, Mohammed Elhassani Charkani (2018)

Commentationes Mathematicae Universitatis Carolinae

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Let $R$ be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over $R$ is a CF-module. When $R$ is local, we characterize the CF-modules over $R$ whose tensor product is a CF-module.

The Grothendieck ring of quantum double of quaternion group

Hua Sun, Jia Pang, Yanxi Shen (2024)

Czechoslovak Mathematical Journal

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Let $𝕜$ be an algebraically closed field of characteristic $p \neq 2$ , and let $Q_{8}$ be the quaternion group. We describe the structures of all simple modules over the quantum double $D (𝕜 Q_{8})$ of group algebra $𝕜 Q_{8}$ . Moreover, we investigate the tensor product decomposition rules of all simple $D (𝕜 Q_{8})$ -modules. Finally, we describe the Grothendieck ring $G_{0} (D (𝕜 Q_{8}))$ by generators with relations.

Melkersson condition on Serre subcategories

Reza Sazeedeh, Rasul Rasuli (2016)

Colloquium Mathematicae

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Let R be a commutative noetherian ring, let be an ideal of R, and let be a subcategory of the category of R-modules. The condition $C_{}$ , defined for R-modules, was introduced by Aghapournahr and Melkersson (2008) in order to study when the local cohomology modules relative to belong to . In this paper, we define and study the class $_{}$ consisting of all modules satisfying $C_{}$ . If and are ideals of R, we get a necessary and sufficient condition for to satisfy $C_{}$ and $C_{}$ simultaneously. We also...

Unimodular rows over Laurent polynomial rings

Abdessalem Mnif, Morou Amidou (2022)

Czechoslovak Mathematical Journal

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We prove that for any ring $𝐑$ of Krull dimension not greater than 1 and $n \geq 3$ , the group $E_{n} (𝐑 [X, X^{- 1}])$ acts transitively on ${Um}_{n} (𝐑 [X, X^{- 1}])$ . In particular, we obtain that for any ring $𝐑$ with Krull dimension not greater than 1, all finitely generated stably free modules over $𝐑 [X, X^{- 1}]$ are free. All the obtained results are proved constructively.

$C^{1, α}$ regularity for elliptic equations with the general nonstandard growth conditions

Sungchol Kim, Dukman Ri (2024)

Mathematica Bohemica

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We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $Ω$ . We prove the global $C^{1, α}$ regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the $C^{1, α}$ regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.

Relative tilting modules with respect to a semidualizing module

Maryam Salimi (2019)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative Noetherian ring, and let $C$ be a semidualizing $R$ -module. The notion of $C$ -tilting $R$ -modules is introduced as the relative setting of the notion of tilting $R$ -modules with respect to $C$ . Some properties of tilting and $C$ -tilting modules and the relations between them are mentioned. It is shown that every finitely generated $C$ -tilting $R$ -module is $C$ -projective. Finally, we investigate some kernel subcategories related to $C$ -tilting modules.

Generalized tilting modules over ring extension

Zhen Zhang (2019)

Czechoslovak Mathematical Journal

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Let $Γ$ be a ring extension of $R$ . We show the left $Γ$ -module $U = Γ \otimes_{R} C$ with the endmorphism ring End $_{Γ} U = Δ$ is a generalized tilting module when $_{R} C$ is a generalized tilting module under some conditions.

Local cohomology, cofiniteness and homological functors of modules

Kamal Bahmanpour (2022)

Czechoslovak Mathematical Journal

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Let $I$ be an ideal of a commutative Noetherian ring $R$ . It is shown that the $R$ -modules $H_{I}^{j} (M)$ are $I$ -cofinite for all finitely generated $R$ -modules $M$ and all $j \in ℕ_{0}$ if and only if the $R$ -modules ${Ext}_{R}^{i} (N, H_{I}^{j} (M))$ and ${Tor}_{i}^{R} (N, H_{I}^{j} (M))$ are $I$ -cofinite for all finitely generated $R$ -modules $M$ , $N$ and all integers $i, j \in ℕ_{0}$ .

Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms

Salvatore Bonafede (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove the local Hölder continuity of bounded generalized solutions of the Dirichlet problem associated to the equation $\sum_{i = 1}^{m} \frac{\partial}{\partial x_{i}} a_{i} (x, u, \nabla u) - c_{0} {| u |}^{p - 2} u = f (x, u, \nabla u),$ assuming that the principal part of the equation satisfies the following degenerate ellipticity condition $λ (| u |) \sum_{i = 1}^{m} a_{i} (x, u, η) η_{i} \geq ν (x) {| η |}^{p},$ and the lower-order term $f$ has a natural growth with respect to $\nabla u$ .

Recollements induced by good (co)silting dg-modules

Rongmin Zhu, Jiaqun Wei (2023)

Czechoslovak Mathematical Journal

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Let $U$ be a dg- $A$ -module, $B$ the endomorphism dg-algebra of $U$ . We know that if $U$ is a good silting object, then there exist a dg-algebra $C$ and a recollement among the derived categories $𝐃 (C, d)$ of $C$ , $𝐃 (B, d)$ of $B$ and $𝐃 (A, d)$ of $A$ . We investigate the condition under which the induced dg-algebra $C$ is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained....

Convex integration and the $L^{p}$ theory of elliptic equations

Kari Astala, Daniel Faraco, László Székelyhidi Jr. (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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This paper deals with the $L^{p}$ theory of linear elliptic partial differential equations with bounded measurable coefficients. We construct in two dimensions examples of weak and so-called very weak solutions, with critical integrability properties, both to isotropic equations and to equations in non-divergence form. These examples show that the general $L^{p}$ theory, developed in [1, 24] and [2], cannot be extended under any restriction on the essential range of the coefficients. Our constructions...

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

El Houssine Azroul, Abdelkrim Barbara, Meryem El Lekhlifi, Mohamed Rhoudaf (2012)

Applicationes Mathematicae

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We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem $- d i v (a (x, u, \nabla u)) + g (x, u) = f - d i v F$ in Ω, where Ω is a bounded open domain of $ℝ^{N}$ , N ≥ 2 and $a : Ω \times ℝ \times ℝ^{N} \to ℝ^{N}$ is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to $\prod_{i = 1}^{N} L^{p^{'} (\cdot)} (Ω)$ .

Fonctions biharmoniques adjointes

Emmanuel P. Smyrnelis (2010)

Annales Polonici Mathematici

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The study of the equation (L₂L₁)*h = 0 or of the equivalent system L*₂h₂ = -h₁, L*₁h₁ = 0, where $L_{j} (j = 1, 2)$ is a second order elliptic differential operator, leads us to the following general framework: Starting from a biharmonic space, for example the space of solutions (u₁,u₂) of the system L₁u₁ = -u₂, L₂u₂ = 0, $L_{j} (j = 1, 2)$ being elliptic or parabolic, and by means of its Green pairs, we construct the associated adjoint biharmonic space which is in duality with the initial one.

Displaying similar documents to “Regularity for elliptic pairs over ℂ [ [ ] ”

Displaying similar documents to “Regularity for elliptic pairs over $ℂ [[]$ ”