Minimal Lp-solutions to singular sublinear elliptic problems
We solve the existence problem for the minimal positive solutions u∈Lp(Ω,dx) to the Dirichlet problems for sublinear elliptic equations of the form Lu=σuq+μinΩ,lim infx→yu(x)=0y∈∂∞Ω,where 0<q<1 and Lu≔−div(A(x)∇u) is a linear uniformly elliptic operator with bounded measurable coefficients. Th...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037423000675 |
| _version_ | 1827316936354037760 |
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| author | Aye Chan May Adisak Seesanea |
| author_facet | Aye Chan May Adisak Seesanea |
| author_sort | Aye Chan May |
| collection | DOAJ |
| description | We solve the existence problem for the minimal positive solutions u∈Lp(Ω,dx) to the Dirichlet problems for sublinear elliptic equations of the form Lu=σuq+μinΩ,lim infx→yu(x)=0y∈∂∞Ω,where 0<q<1 and Lu≔−div(A(x)∇u) is a linear uniformly elliptic operator with bounded measurable coefficients. The coefficient σ and data μ are nonnegative Radon measures on an arbitrary domain Ω⊂Rn with a positive Green function associated with L. Our techniques are based on the use of sharp Green potential pointwise estimates, weighted norm inequalities, and norm estimates in terms of generalized energy. |
| first_indexed | 2024-03-09T01:27:33Z |
| format | Article |
| id | doaj.art-a6c42d7aac9d41ce89c24b10cce5cc3b |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-24T23:24:04Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-a6c42d7aac9d41ce89c24b10cce5cc3b2024-03-16T05:09:06ZengElsevierResults in Applied Mathematics2590-03742024-02-0121100421Minimal Lp-solutions to singular sublinear elliptic problemsAye Chan May0Adisak Seesanea1School of Integrated Science and Innovation, Sirindhorn International Institute of Technology, Thammasat University, ThailandCorresponding author.; School of Integrated Science and Innovation, Sirindhorn International Institute of Technology, Thammasat University, ThailandWe solve the existence problem for the minimal positive solutions u∈Lp(Ω,dx) to the Dirichlet problems for sublinear elliptic equations of the form Lu=σuq+μinΩ,lim infx→yu(x)=0y∈∂∞Ω,where 0<q<1 and Lu≔−div(A(x)∇u) is a linear uniformly elliptic operator with bounded measurable coefficients. The coefficient σ and data μ are nonnegative Radon measures on an arbitrary domain Ω⊂Rn with a positive Green function associated with L. Our techniques are based on the use of sharp Green potential pointwise estimates, weighted norm inequalities, and norm estimates in terms of generalized energy.http://www.sciencedirect.com/science/article/pii/S2590037423000675Sublinear elliptic equationMeasure dataDivergence form operatorGreen function |
| spellingShingle | Aye Chan May Adisak Seesanea Minimal Lp-solutions to singular sublinear elliptic problems Results in Applied Mathematics Sublinear elliptic equation Measure data Divergence form operator Green function |
| title | Minimal Lp-solutions to singular sublinear elliptic problems |
| title_full | Minimal Lp-solutions to singular sublinear elliptic problems |
| title_fullStr | Minimal Lp-solutions to singular sublinear elliptic problems |
| title_full_unstemmed | Minimal Lp-solutions to singular sublinear elliptic problems |
| title_short | Minimal Lp-solutions to singular sublinear elliptic problems |
| title_sort | minimal lp solutions to singular sublinear elliptic problems |
| topic | Sublinear elliptic equation Measure data Divergence form operator Green function |
| url | http://www.sciencedirect.com/science/article/pii/S2590037423000675 |
| work_keys_str_mv | AT ayechanmay minimallpsolutionstosingularsublinearellipticproblems AT adisakseesanea minimallpsolutionstosingularsublinearellipticproblems |