Annali di Matematica Pura ed Applicata最新文献_第3页

Refining Hölder regularity theory in degenerate drift-diffusion equations 改进退化漂移扩散方程中的Hölder正则性理论

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-14 DOI: 10.1007/s10231-025-01642-4

Tobias Black

{"title":"Refining Hölder regularity theory in degenerate drift-diffusion equations","authors":"Tobias Black","doi":"10.1007/s10231-025-01642-4","DOIUrl":"10.1007/s10231-025-01642-4","url":null,"abstract":"<div>\u0000 \u0000 <p>We establish the Hölder continuity of bounded nonnegative weak solutions to </p><div><div><span>$$begin{aligned} big (Phi ^{-1}(w)big )_t=Delta w+nabla cdot big (a(x,t)Phi ^{-1}(w)big )+bbig (x,t,Phi ^{-1}(w)big ), end{aligned}$$</span></div></div><p>with convex <span>(Phi in C^0([0,infty ))cap C^2((0,infty )))</span> satisfying <span>(Phi (0)=0)</span>, <span>(Phi^{prime}>0)</span> on <span>((0,infty ))</span> and </p><div><div><span>$$begin{aligned} sPhi^{primeprime}(s)le CPhi^{prime}(s)quad text {for all }sin [0,s_0] end{aligned}$$</span></div></div><p>for some <span>(C>0)</span> and <span>(s_0in (0,1])</span>. The functions <i>a</i> and <i>b</i> are only assumed to satisfy integrability conditions of the form </p><div><div><span>$$begin{aligned} a&in L^{2q_1}big ((0,T);L^{2q_2}(Omega ;mathbb {R}^N)big ), b&in Mbig (Omega _Ttimes mathbb {R}big ) text {such that }big |b(x,t,xi )big |le {hat{b}}(x,t) text {a.e. for some }{hat{b}}in L^{q_1}big ((0,T);L^{q_2}(Omega )big ) end{aligned}$$</span></div></div><p>with <span>(q_1,q_2>1)</span> such that </p><div><div><span>$$begin{aligned} frac{2}{q_1}+frac{N}{q_2}=2-Nkappa quad text {for some }kappa in (0,tfrac{2}{N}). end{aligned}$$</span></div></div><p>Letting <span>(w=Phi (u))</span> and assuming the inverse <span>(Phi ^{-1}:[0,infty )rightarrow [0,infty ))</span> to be locally Hölder continuous, this entails Hölder regularity for bounded weak solutions of </p><div><div><span>$$begin{aligned} u_t=Delta Phi (u)+nabla cdot big (a(x,t)ubig )+b(x,t,u) end{aligned}$$</span></div></div><p>and, accordingly, covers a wide array of taxis type structures. In particular, many chemotaxis frameworks with nonlinear diffusion, which cannot be covered by the standard literature, fall into this category. After rigorously treating local Hölder regularity, we also extend the regularity result to the associated initial-boundary value problem for boundary conditions of flux-type.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 3","pages":"1397 - 1463"},"PeriodicalIF":0.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01642-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148268637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Kernel estimates for a class of fractional Kolmogorov operators 一类分数阶Kolmogorov算子的核估计

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-14 DOI: 10.1007/s10231-025-01653-1

Marianna Porfido, Abdelaziz Rhandi, Cristian Tacelli

引用次数: 0

Positioned and primary positioned (mathcal {C})-semigroups 定位和主定位(mathcal {C}) -半群

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-13 DOI: 10.1007/s10231-025-01634-4

C. Cisto, R. Tapia-Ramos

引用次数: 0

Anisotropic lower-dimensional Minkowski content and (mathcal{S}text{-content}) 各向异性低维闵可夫斯基含量和 (mathcal{S}text{-content})

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-13 DOI: 10.1007/s10231-025-01650-4

Filip Fryš

引用次数: 0

Global existence and blow-up phenomena for the periodic problem about a family of Camassa-Holm type equation with both dissipation and dispersion 一类既有耗散又有色散的Camassa-Holm型方程周期问题的整体存在性和爆破现象

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-06 DOI: 10.1007/s10231-025-01647-z

Min Zhu, Chen Han, Ying Wang

引用次数: 0

The bielliptic locus in the Hilbert scheme of canonical curves is unirational 典型曲线Hilbert格式中的双椭圆轨迹是单方的

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-06 DOI: 10.1007/s10231-025-01643-3

Andrei Stoenică

引用次数: 0

Intrinsic characterization of projective special complex manifolds 射影特殊复流形的内在表征

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-05 DOI: 10.1007/s10231-025-01626-4

Vicente Cortés, Kazuyuki Hasegawa

{"title":"Intrinsic characterization of projective special complex manifolds","authors":"Vicente Cortés, Kazuyuki Hasegawa","doi":"10.1007/s10231-025-01626-4","DOIUrl":"10.1007/s10231-025-01626-4","url":null,"abstract":"<div><p>We define the notion of an <span>(S^1)</span>-bundle of projective special complex base type and construct a conical special complex manifold from it. Consequently the base space of such an <span>(S^{1})</span>-bundle can be realized as <span>({mathbb {C}}^{*})</span>-quotient of a conical special complex manifold. As a corollary, we give an intrinsic characterization of a projective special complex manifold generalizing Mantegazza’s characterization of a projective special Kähler manifold. Our characterization is in the language of c-projective structures. As an application, a non-trivial <span>(S^1)</span>-family of Obata-Ricci-flat hypercomplex structures (given by a generalization of the rigid c-map) on the tangent bundle of the total space of a <span>({mathbb {C}}^*)</span>-bundle over a complex manifold with certain kind of c-projective structure is constructed. Finally, we show that the quaternionic structure underlying any of these hypercomplex structures is in general not flat and that its flatness implies the vanishing of the c-projective Weyl tensor of the base of the <span>({mathbb {C}}^*)</span>-bundle. Conversely, any c-projectively flat complex manifold satisfying a cohomological integrality condition gives rise to a flat quaternionic structure.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 2","pages":"849 - 901"},"PeriodicalIF":0.9,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Symmetric rank of some reducible quartics 一些可约四分数的对称秩

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-01-02 DOI: 10.1007/s10231-025-01648-y

Liena Colarte-Gómez, Francesco Galuppi

引用次数: 0

Blow up phenomenon and sharp ill-posedness for the short-pulse equation 短脉冲方程的爆破现象和尖锐病态

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-29 DOI: 10.1007/s10231-025-01649-x

Yingying Guo, Min Li, Yue Liu, Weikui Ye, Zhaoyang Yin

引用次数: 0

Quantitative unique continuation property for fourth-order Baouendi-Grushin type subelliptic operators with a potential 具有势的四阶Baouendi-Grushin型次椭圆算子的定量唯一连续性

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-24 DOI: 10.1007/s10231-025-01645-1

Yusheng Qiu, Jinggang Tan, Aliang Xia

{"title":"Quantitative unique continuation property for fourth-order Baouendi-Grushin type subelliptic operators with a potential","authors":"Yusheng Qiu, Jinggang Tan, Aliang Xia","doi":"10.1007/s10231-025-01645-1","DOIUrl":"10.1007/s10231-025-01645-1","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate the quantitative unique continuation property for solutions to </p><div><div><span>$$begin{aligned} Delta ^2_{X} u = V u, end{aligned}$$</span></div></div><p>where <span>(Delta _{X} = Delta _{x} + |x|^{2beta } Delta _{y})</span> (<span>(0 < beta le 1)</span>), with <span>(x in mathbb {R}^{m})</span> and <span>(y in mathbb {R}^{n})</span>, denotes a class of subelliptic operators of Baouendi-Grushin type. The potential <i>V</i> is assumed to be bounded and satisfy <span>(|Z V| le K psi )</span> for some constant <span>(K>0)</span>, where <span>(Z= sum _{i=1}^m x_i partial _{x_i} + (beta +1)sum _{j=1}^n y_j partial _{y_j})</span>, <span>(psi )</span> is the angle function given by <span>(psi = frac{|x|^{2beta }}{rho ^{2beta }})</span>, and </p><div><div><span>$$begin{aligned} rho (x,y) = left( |x|^{2(beta +1)} + (beta +1)^2 |y|^2right) ^{frac{1}{2(beta +1)}} end{aligned}$$</span></div></div><p>defines the associated pseudo-gauge. By adapting Almgren’s approach, we establish an almost monotonicity formula for the frequency function. As a consequence, we derive a quantitative unique continuation result for solutions to the fourth-order subelliptic equation.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 3","pages":"1509 - 1539"},"PeriodicalIF":0.9,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148268746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0