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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2604.01544 |
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| _version_ | 1866917387410866176 |
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| author | Xiao, Botian Tang, Lin |
| author_facet | Xiao, Botian Tang, Lin |
| contents | In this paper we discuss the solvability of the Neumann and Regularity boundary value problem of elliptic Schrödinger-type equation $-\DIV(A(x)\nabla u(x,t))+V(x)u(x,t)=0$ with bounded measurable uniformly elliptic coefficinets $A(x)$ independent of $t$ and $V$ in Reverse Hölder class $\mathcal{B}_q$, and Neumann boundary data $\partial_{ν_A}u(x,0)=f(x)\in H^p_{\mathcal{L}}(\rn)$, or Regularity data $u(x,0)=g\in H^{1,p}_V(\rn)$, utilizing the method of layer potential. We prove the solvability when $A$ is a small $L^\infty$ perturbation of a matrix satisfying De Giorgi-Nash-Moser bounds. Besides we also give the Campanato norm estimate of the double layer potential related to the Dirichlet problem with boundary data in certain Campanato-type spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01544 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solvability of boundary value problem for Schrödinger Equations with Reverse Hölder Potentials on $L^p$ and endpoint spaces Xiao, Botian Tang, Lin Analysis of PDEs In this paper we discuss the solvability of the Neumann and Regularity boundary value problem of elliptic Schrödinger-type equation $-\DIV(A(x)\nabla u(x,t))+V(x)u(x,t)=0$ with bounded measurable uniformly elliptic coefficinets $A(x)$ independent of $t$ and $V$ in Reverse Hölder class $\mathcal{B}_q$, and Neumann boundary data $\partial_{ν_A}u(x,0)=f(x)\in H^p_{\mathcal{L}}(\rn)$, or Regularity data $u(x,0)=g\in H^{1,p}_V(\rn)$, utilizing the method of layer potential. We prove the solvability when $A$ is a small $L^\infty$ perturbation of a matrix satisfying De Giorgi-Nash-Moser bounds. Besides we also give the Campanato norm estimate of the double layer potential related to the Dirichlet problem with boundary data in certain Campanato-type spaces. |
| title | Solvability of boundary value problem for Schrödinger Equations with Reverse Hölder Potentials on $L^p$ and endpoint spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.01544 |