Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU147909" target="_blank" >RIV/00216305:26220/24:PU147909 - isvavai.cz</a>
Result on the web
<a href="https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001" target="_blank" >https://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00208-023-02593-y" target="_blank" >10.1007/s00208-023-02593-y</a>
Alternative languages
Result language
angličtina
Original language name
Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MATHEMATISCHE ANNALEN
ISSN
0025-5831
e-ISSN
1432-1807
Volume of the periodical
388
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
41
Pages from-to
2519-2559
UT code for WoS article
000940224800001
EID of the result in the Scopus database
2-s2.0-85148859851