Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements
| Autor: | Ghosh, Suchandan, Kumar, Dharmendra, Prasad, Harsh, Tewary, Vivek |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove existence of variational solutions for a class of doubly nonlinear nonlocal evolution equations whose prototype is the double phase equation \begin{align*} \partial_t u^m &+ \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}}\\&+a(x,y)\frac{|u(x,t)-u(y,t)|^{q-2}(u(x,t)-u(y,t))}{|x-y|^{N+qr}} \,dy = 0,\,m>0,\,p>1,\,s,r\in (0,1). \end{align*} We make use of the approach of minimizing movements pioneered by DeGiorgi and Ambrosio and refined by B\"ogelein, Duzaar, Marcellini, and co-authors to study nonlinear parabolic equations with non-standard growth. Comment: 39 pages. arXiv admin note: text overlap with arXiv:2112.00402 |
| Databáze: | arXiv |
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