Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation
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Date
2024-01-15
Authors
Fang, Yuzhou
Radulescu, Vicentiu
Zhang, Chao
ORCID
0000-0003-4615-5537Advisor
Referee
Mark
Journal Title
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Volume Title
Publisher
Springer Nature
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Abstract
We establish the equivalence between weak and viscosity solutions to the nonhomogeneous double phase equation with lower-order term - div(|Du|(p-2)Du+a(x)|Du|(q-2)Du)= f (x, u, Du), 1 < p <= q < infinity, a(x) >= 0. We find some appropriate hypotheses on the coefficient a(x), the exponents p, q and the nonlinear term f to show that the viscosity solutions with a priori Lipschitz continuity are weak solutions of such equation by virtue of the inf(sup)-convolution techniques. The reverse implication can be concluded through comparison principles. Moreover, we verify that the bounded viscosity solutions are exactly Lipschitz continuous, which is also of independent interest.
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Citation
MATHEMATISCHE ANNALEN. 2024, vol. 388, issue 3, p. 2519-2559.
https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001
https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001
Document type
Peer-reviewed
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Published version
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en