Nonlinear elliptic equations with variable exponent: old and new

VD Rădulescu - Nonlinear Analysis: Theory, Methods & Applications, 2015 - Elsevier
In this survey paper, by using variational methods, we are concerned with the qualitative
analysis of solutions to nonlinear elliptic problems of the type {− div A (x,∇ u)= λ| u| q (x)− 2 …

Regularity for minimizers for functionals of double phase with variable exponents

MA Ragusa, A Tachikawa - Advances in Nonlinear Analysis, 2019 - degruyter.com
The functionals of double phase type H (u):=∫| D u| p+ a (x)| D u| qdx,(q> p> 1, a (x)≥ 0) are
introduced in the epoch-making paper by Colombo-Mingione for constants p and q, and …

Regularity for general functionals with double phase

P Baroni, M Colombo, G Mingione - Calculus of Variations and Partial …, 2018 - Springer
We prove sharp regularity results for a general class of functionals of the type w ↦ ∫ F (x, w,
Dw)\, dx, w↦∫ F (x, w, D w) dx, featuring non-standard growth conditions and non-uniform …

Regularity for double phase variational problems

M Colombo, G Mingione - Archive for Rational Mechanics and Analysis, 2015 - Springer
We prove sharp regularity theorems for minimisers of a class of variational integrals whose
integrand switches between two different types of degenerate elliptic phases, according to …

[PDF][PDF] Bounded minimisers of double phase variational integrals

M Colombo, G Mingione - Arch. Ration. Mech. Anal, 2015 - researchgate.net
Definition 1 implies that local minimisers are automatically in W 1, p loc (Ω). We immediately
say that since all the regularity properties of local minimisers treated in this paper are local in …

[图书][B] Lebesgue and Sobolev spaces with variable exponents

L Diening, P Harjulehto, P Hästö, M Ruzicka - 2011 - books.google.com
The field of variable exponent function spaces has witnessed an explosive growth in recent
years. The standard reference article for basic properties is already 20 years old. Thus this …

Harnack inequalities for double phase functionals

P Baroni, M Colombo, G Mingione - Nonlinear Analysis: Theory, Methods & …, 2015 - Elsevier
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Non-autonomous functionals, borderline cases and related function classes

P Baroni, M Colombo, G Mingione - St. Petersburg Mathematical Journal, 2016 - ams.org
The class of non-autonomous functionals under study is characterized by the fact that the
energy density changes its ellipticity and growth properties according to the point; some …

Regularity results for stationary electro-rheological fluids

E Acerbi, G Mingione - Archive for rational mechanics and analysis, 2002 - Springer
We prove regularity results for weak solutions to systems modelling electro-rheological fluids
in the stationary case, as proposed in [27, 31]; a particular case of the system we consider is …

[PDF][PDF] Maximal function on generalized Lebesque spaces L^ P^(^⊙^)

L Diening - Mathematical Inequalities and Applications, 2004 - researchgate.net
MAXIMAL FUNCTION ON GENERALIZED LEBESGUE SPACES LP) Page 1 fherr) CfjCC|
equClifies :pplications Vīnē 7 Nürnber 2 (2003), 245-253 MAXIMAL FUNCTION ON …