A new class of double phase variable exponent problems: Existence and uniqueness
By Ángel Crespo-Blanco, Leszek Gasinski, Petteri Harjulehto, Patrick Winkert. Journal of Differential Equations, 2021
228 citations recorded by the source corpus.
In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties of the corresponding Musielak-Orlicz Sobolev spaces (an equivalent norm, uniform convexity, Radon-Riesz property with respect to the modular) and the properties of the new double phase operator (continuity, strict monotonicity, (S$_+$)-property). In contrast to the known constant exponent case we are able to weaken the assumptions on the data. Finally we show the existence and uniqueness of corresponding elliptic equations with right-hand sides that have gradient dependence (so-called convection terms) under very general assumptions on the data. As a result of independent interest, we also show the density of smooth functions in the new Musielak-Orlicz Sobolev space even when the domain is unbounded.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/0c882f79ac8e52bc8c16ff0ecb4c76a7a33e117c
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Citations in the corpus
- Existence of solutions for singular double phase problems via the Nehari manifold method (2021, unknown): “18(ii) of Crespo–Blanco–Gasiński–Harjulehto–Winkert [17].”
- New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, background): “The following embedding results can be found in [16].”