Publication detail

Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation

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"
}