Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910528288325632 |
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| author | Cianchi, Andrea Diebou, Gael Y. Slavíková, Lenka |
| author_facet | Cianchi, Andrea Diebou, Gael Y. Slavíková, Lenka |
| contents | Existence and global regularity results for boundary-value problems of Robin type for harmonic and polyharmonic functions in $n$-dimensional half-spaces are offered. The Robin condition on the normal derivative on the boundary of the half-space is prescribed by a nonlinear function $\mathcal N$ of the relevant harmonic or polyharmonic functions. General Orlicz type growths for the function $\mathcal N$ are considered. For instance, functions $\mathcal N$ of classical power type, their perturbations by logarithmic factors, and exponential functions are allowed. New sharp boundedness properties in Orlicz spaces of some classical operators from harmonic analysis, of independent interest, are critical for our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space Cianchi, Andrea Diebou, Gael Y. Slavíková, Lenka Analysis of PDEs Existence and global regularity results for boundary-value problems of Robin type for harmonic and polyharmonic functions in $n$-dimensional half-spaces are offered. The Robin condition on the normal derivative on the boundary of the half-space is prescribed by a nonlinear function $\mathcal N$ of the relevant harmonic or polyharmonic functions. General Orlicz type growths for the function $\mathcal N$ are considered. For instance, functions $\mathcal N$ of classical power type, their perturbations by logarithmic factors, and exponential functions are allowed. New sharp boundedness properties in Orlicz spaces of some classical operators from harmonic analysis, of independent interest, are critical for our approach. |
| title | Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.15257 |