Detail publikace

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

FANG, Y. RADULESCU, V. ZHANG, C.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

regularity; functionals

Autoři

FANG, Y.; RADULESCU, V.; ZHANG, C.

Vydáno

15. 1. 2024

Nakladatel

Springer Nature

ISSN

0025-5831

Periodikum

MATHEMATISCHE ANNALEN

Ročník

388

Číslo

3

Stát

Spolková republika Německo

Strany od

2519

Strany do

2559

Strany počet

41

URL

https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001

Plný text v Digitální knihovně

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"
}