تقرير
On a quasilinear elliptic problem involving the 1-laplacian operator and a discontinuous nonlinearity
| العنوان: | On a quasilinear elliptic problem involving the 1-laplacian operator and a discontinuous nonlinearity |
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| المؤلفون: | Pimenta, Marcos T. O., Santos, Gelson C. G., Júnior, João R. Santos |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35J62, 35J75, B.2 |
| الوصف: | In this work, we study a quasilinear elliptic problem involving the 1-laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function $H(\cdot - \beta)$. Our approach is based on an analysis of the associated p-laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as $p \to 1^+$. We study also the asymptotic behaviour of the solutions, as $\beta \to 0^+$ and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity. Comment: 21 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2210.10889 |
| رقم الأكسشن: | edsarx.2210.10889 |
| قاعدة البيانات: | arXiv |
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