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FANG, Y. RADULESCU, V. ZHANG, C.
Original Title
Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation
Type
journal article in Web of Science
Language
English
Original 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.
Keywords
regularity; functionals
Authors
FANG, Y.; RADULESCU, V.; ZHANG, C.
Released
15. 1. 2024
Publisher
Springer Nature
ISBN
0025-5831
Periodical
MATHEMATISCHE ANNALEN
Year of study
388
Number
3
State
Federal Republic of Germany
Pages from
2519
Pages to
2559
Pages count
41
URL
https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001
Full text in the Digital Library
http://hdl.handle.net/11012/244281
BibTex
@article{BUT183167, author="Yuzhou {Fang} and Vicentiu {Radulescu} and Chao {Zhang}", title="Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation", journal="MATHEMATISCHE ANNALEN", year="2024", volume="388", number="3", pages="41", doi="10.1007/s00208-023-02593-y", issn="0025-5831", url="https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001" }