Orlicz空间中非齐次分式方程的弱解和粘性解

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2021-12-06 DOI:10.57262/ade027-1112-735

Maria L. de Borb'on, Leandro Martin Del Pezzo, Pablo Ochoa

{"title":"Orlicz空间中非齐次分式方程的弱解和粘性解","authors":"Maria L. de Borb'on, Leandro Martin Del Pezzo, Pablo Ochoa","doi":"10.57262/ade027-1112-735","DOIUrl":null,"url":null,"abstract":"In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function and its fractional gradient. The latter is adapted to the Orlicz framework. The main contribution of the article is to establish the equivalence between weak and viscosity solutions for such equations.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Weak and viscosity solutions for non-homogeneous fractional equations in Orlicz spaces\",\"authors\":\"Maria L. de Borb'on, Leandro Martin Del Pezzo, Pablo Ochoa\",\"doi\":\"10.57262/ade027-1112-735\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function and its fractional gradient. The latter is adapted to the Orlicz framework. The main contribution of the article is to establish the equivalence between weak and viscosity solutions for such equations.\",\"PeriodicalId\":53312,\"journal\":{\"name\":\"Advances in Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2021-12-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.57262/ade027-1112-735\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/ade027-1112-735","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 4

摘要

在本文中，我们考虑了Orlicz空间中的非齐次分式方程，其源取决于空间变量、未知函数及其分数梯度。后者适用于Orlicz框架。本文的主要贡献是建立了这类方程的弱解和粘性解之间的等价性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Weak and viscosity solutions for non-homogeneous fractional equations in Orlicz spaces

In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function and its fractional gradient. The latter is adapted to the Orlicz framework. The main contribution of the article is to establish the equivalence between weak and viscosity solutions for such equations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.