On variational problems and nonlinear elliptic equations with nonstandard growth conditions

By V. Zhikov. 2011

261 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2c01aef05e5c3a6f5ca7d91befe886c2004b1bc6

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Some Approximation Properties in Musielak-Orlicz-Sobolev Spaces (2012, result): “…m 0 L ϕ (Ω) for the modular convergence, under the Our result generalizes that of the authors in [2] in the case of Musielak-Orlicz-Sobolev spaces, that of Gossez in [3] in the case of classical Orlicz spaces and those of Zhikov [4] [5] and Samko [6] in the case of variable exponent Sobolev spaces.”
Multiple solutions for parametric double phase Dirichlet problems (2020, background): “Such functionals were first investigated in the context of problems of the calculus of variations and of elasticity theory by Marcellini [10, 11] and Zhikov [18, 19].”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, background): “For example, in the elasticity theory, the modulating coefficient μ(·) dictates the geometry of composites made of two different materials with distinct power hardening exponents q and p, see Zhikov [52].”
On double phase Kirchhoff problems with singular nonlinearity (2021, background): “4) has several mathematical applications in the study of duality theory and of the Lavrentiev gap phenomenon, see Zhikov [38,39].”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “See e.g. [200, Example 3.2] by Zhikov with p(·) being a step function.”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, background): “For example, in the elasticity theory, the modulating coefficient μ(·) dictates the geometry of composites made of two different materials with distinct power hardening exponents q(x) and p(x), see Zhikov [71].”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, background): “For example, in the elasticity theory, the modulating coefficient μ(·) dictates the geometry of composites made of two different materials with distinct power hardening exponents q(x) and p(x), see Zhikov [72].”