Interior $W^{2,δ}$ type estimates for degenerate fully nonlinear elliptic equations with $L^n$ data
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913571867197440 |
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| author | Byun, Sun-Sig Kim, Hongsoo Oh, Jehan |
| author_facet | Byun, Sun-Sig Kim, Hongsoo Oh, Jehan |
| contents | We establish interior $W^{2,δ}$ type estimates for a class of degenerate fully nonlinear elliptic equations with $L^n$ data. The main idea of our approach is to slide $C^{1,α}$ cones, instead of paraboloids, vertically to touch the solution, and estimate the contact set in terms of the measure of the vertex set. This shows that the solution has tangent $C^{1,α}$ cones almost everywhere, which leads to the desired Hessian estimates. Accordingly, we are able to develop a kind of counterpart to the estimates for divergent structure quasilinear elliptic problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02846 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior $W^{2,δ}$ type estimates for degenerate fully nonlinear elliptic equations with $L^n$ data Byun, Sun-Sig Kim, Hongsoo Oh, Jehan Analysis of PDEs 35B65, 35D40, 35J60, 35J70 We establish interior $W^{2,δ}$ type estimates for a class of degenerate fully nonlinear elliptic equations with $L^n$ data. The main idea of our approach is to slide $C^{1,α}$ cones, instead of paraboloids, vertically to touch the solution, and estimate the contact set in terms of the measure of the vertex set. This shows that the solution has tangent $C^{1,α}$ cones almost everywhere, which leads to the desired Hessian estimates. Accordingly, we are able to develop a kind of counterpart to the estimates for divergent structure quasilinear elliptic problems. |
| title | Interior $W^{2,δ}$ type estimates for degenerate fully nonlinear elliptic equations with $L^n$ data |
| topic | Analysis of PDEs 35B65, 35D40, 35J60, 35J70 |
| url | https://arxiv.org/abs/2411.02846 |