Schrödinger type equations with singular coefficients and lower order terms
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916122520977408 |
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| author | Junior, Alexandre Arias Ascanelli, Alessia Cappiello, Marco Garetto, Claudia |
| author_facet | Junior, Alexandre Arias Ascanelli, Alessia Cappiello, Marco Garetto, Claudia |
| contents | In this paper we investigate the well-posedness of the Cauchy problem for a Schrödinger operator with singular lower order terms. We allow distributional coefficients and we approach this problem via the regularising methods at the core of the theory of very weak solutions. We prove that a very weak solution exists and it is unique modulo negligible perturbations. Very weak solutions converge to classical solutions when the equation coefficients are regular enough. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schrödinger type equations with singular coefficients and lower order terms Junior, Alexandre Arias Ascanelli, Alessia Cappiello, Marco Garetto, Claudia Analysis of PDEs Primary 35J10, Secondary 35D99 In this paper we investigate the well-posedness of the Cauchy problem for a Schrödinger operator with singular lower order terms. We allow distributional coefficients and we approach this problem via the regularising methods at the core of the theory of very weak solutions. We prove that a very weak solution exists and it is unique modulo negligible perturbations. Very weak solutions converge to classical solutions when the equation coefficients are regular enough. |
| title | Schrödinger type equations with singular coefficients and lower order terms |
| topic | Analysis of PDEs Primary 35J10, Secondary 35D99 |
| url | https://arxiv.org/abs/2402.07826 |