On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian

Santos, E. B. dos; Leitão, Raimundo

doi:10.1007/s42985-021-00083-x

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…Both studies in [4,37] exploited the geometric aspect of the jump measure, which differs from π(dy) in (1.1). In [19], the Hölder regularity theory with operators more general than L 2 was also investigated.…”

Section: ˆR3mentioning

confidence: 99%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

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Since the Seoul Metropolitan Area, Republic of Korea, is highly populated, a large number of people are frequently exposed to high concentrations of particulate matter (PM) with mean aerodynamic diameters of <= 10 mm (PM10) in cold season. The concentration of PM10 in Seoul Metropolitan Area increases by transboundary transport, local direct emissions, and chemical reactions of aerosol precursors in the atmosphere. Here, the Seoul Metropolitan Area (Seoul, Gyeonggi-do, and Incheon) and surrounding region (Chungcheongnam-do, Daejeon, and Sejong) are regionally classified by clustering analysis based on the variability of PM10 concentrations. According to the inertia score by the number of clusters, the optimum cluster number of regional variability of PM10 is four. The region of cluster 1 is divided into southern Gyeonggi-do and eastern Chungcheongnam-do, the cluster 2 is mainly classified Incheon, western Gyeonggi-do, and Seoul. The cluster 3 region is western Chungcheongnam-do adjacent to Yellow Sea, and the cluster 4 is classified into eastern Gyeonggi-do. The variability of PM10 in each region is distinguished by the local chemical pollutants emission and weather conditions such as wind speed and direction in each region. This regional classification of PM10 variability is different from administrative districts. Considering most of policies for responding to high concentrations of PM10 are being prepared by administrative districts, this study suggests that a response on the basis of these regional PM10 distribution would be more effective way to improve air quality in the Seoul Metropolitan and Chungcheong Area.

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Section: ˆR3mentioning

confidence: 99%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

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show abstract

“…We refer the reader to [51] for regularity results concerning the fractional Laplacian and to [40] for the fractional p-Laplacian. See also [23] for the anisotropic case. Even in the most simple case, that is p = 2 and s = s 1 = s 2 = • • • = s n , regularity estimates for operators in non-divergence form of the type (1.2) with µ = µ axes lead to various open problems such as an Alexandrov-Bakelmann-Pucci estimate.…”

Section: Introductionmentioning

confidence: 99%

Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order

Chaker¹,

Kim²

2021

Preprint

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$$L_{p}$$-Estimates for Solutions of Equations Governed by Operators like the Anisotropic Fractional Laplacian

Leitão

2023

Bull Braz Math Soc, New Series

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On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian

Cited by 5 publications

References 16 publications

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order

$$L_{p}$$-Estimates for Solutions of Equations Governed by Operators like the Anisotropic Fractional Laplacian

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