Comparison Principle, A.B.P.-type estimates for solutions of quasi-linear elliptic equations in non-divergence form and some implications
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916917811347456 |
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| author | Bessa, Junior da S. Biswas, Reshmi da Silva, João Vitor Sá, Ginaldo Santos, Makson |
| author_facet | Bessa, Junior da S. Biswas, Reshmi da Silva, João Vitor Sá, Ginaldo Santos, Makson |
| contents | In this work, we establish global gradient estimates to solutions of quasilinear elliptic models in non-divergence form with general degeneracy law and a Hamiltonian term, given by $$ -Ψ(x, |\nabla u|)Δ_p^{\mathrm{N}}u(x)+\mathscr{H}(x,\nabla u)=f(x) \quad \mathrm{in} \quad Ω, \quad \mathrm{for} \,\,\,1<p< \infty, $$ under suitable assumptions on the data of the problem. Particularly, our results are relevant for a class of quasi-linear models with Hamiltonian terms. Additionally, we address non-degeneracy estimates for such solutions and present a couple of applications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison Principle, A.B.P.-type estimates for solutions of quasi-linear elliptic equations in non-divergence form and some implications Bessa, Junior da S. Biswas, Reshmi da Silva, João Vitor Sá, Ginaldo Santos, Makson Analysis of PDEs In this work, we establish global gradient estimates to solutions of quasilinear elliptic models in non-divergence form with general degeneracy law and a Hamiltonian term, given by $$ -Ψ(x, |\nabla u|)Δ_p^{\mathrm{N}}u(x)+\mathscr{H}(x,\nabla u)=f(x) \quad \mathrm{in} \quad Ω, \quad \mathrm{for} \,\,\,1<p< \infty, $$ under suitable assumptions on the data of the problem. Particularly, our results are relevant for a class of quasi-linear models with Hamiltonian terms. Additionally, we address non-degeneracy estimates for such solutions and present a couple of applications. |
| title | Comparison Principle, A.B.P.-type estimates for solutions of quasi-linear elliptic equations in non-divergence form and some implications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.18495 |