An Extended Variational Theory for Nonlinear Evolution Equations via Modular Spaces
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Publication:4958022
DOI10.1137/20M1385251zbMath1479.35015arXiv2012.05518MaRDI QIDQ4958022
Alexander Menovschikov, Luca Scarpa, Anastasia Molchanova
Publication date: 6 September 2021
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.05518
Abstract parabolic equations (35K90) PDEs with multivalued right-hand sides (35R70) Variational methods applied to PDEs (35A15) Weak solutions to PDEs (35D30) Singular parabolic equations (35K67)
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Cites Work
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- A Pata-type fixed point theorem in modular spaces with application
- Stochastic partial differential equations: an introduction
- Weighted energy-dissipation functionals for doubly nonlinear evolution
- Analyticity and polynomial approximation in modular function spaces
- Existence for semilinear parabolic stochastic equations
- Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces
- Stochastic porous media equations
- Orlicz spaces and modular spaces
- Convexity inequalities for positive operators
- Renormalized solutions to nonlinear parabolic problems in generalized Musielak-Orlicz spaces
- Overview of differential equations with non-standard growth
- Renormalized solutions for a nonlinear parabolic equation with variable exponents and \(L^{1}\)-data
- Well-posedness and long-time behavior for a class of doubly nonlinear equations
- On some doubly nonlinear evolution equations in Banach spaces
- On the relation of the operator \(\partial/\partial s+partial/\tau\) to evolution governed by accretive operators
- A variational approach to dissipative SPDEs with singular drift
- A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces
- Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces
- Singular stochastic Allen-Cahn equations with dynamic boundary conditions
- A note on doubly nonlinear SPDEs with singular drift in divergence form
- Orlicz spaces and generalized Orlicz spaces
- On the stochastic Cahn-Hilliard equation with a singular double-well potential
- Strong solutions for stochastic partial differential equations of gradient type
- Evolution inclusions governed by subdifferentials in reflexive Banach spaces
- Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions
- On a class of doubly nonlinear nonlocal evolution equations
- The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit
- Fixed point theorems for asymptotically regular mappings in modular and metric spaces
- Strong solutions to SPDEs with monotone drift in divergence form
- Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
- Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and \(L^{1}\) data
- New characterizations of Musielak-Orlicz-Sobolev spaces via sharp ball averaging functions
- Nonlinear semigroups in Hilbert space
- Nonlinear semigroups and evolution equations
- Linear and quasilinear elliptic equations
- Semi-groups of nonlinear contractions and dissipative sets
- Differentiability of nonlinear semigroups
- Orlicz-Sobolev spaces and imbedding theorems
- Solutions faibles d'équations d'évolution dans les espaces de Hilbert. (Weak solution of evolution equations in Hilbert spaces)
- Problèmes unilateraux
- Generalized Orlicz spaces and related PDE
- Doubly Nonlinear Equations as Convex Minimization
- Metric Modular Spaces
- Weighted energy-dissipation functionals for gradient flows
- Fixed point theory in modular function spaces
- On modular spaces
- Some approximation results in Musielak-Orlicz spaces
- On A Class Of Doubly Nonlinear Evolution Equations
- Implicit Degenerate Evolution Equations and Applications
- A First Course in Sobolev Spaces
- Refined existence and regularity results for a class of semilinear dissipative SPDEs
- Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
- Parabolic Equations in Orlicz Spaces
- Nonlinear Differential Equations of Monotone Types in Banach Spaces
- Nonlinear evolution equations in Banach spaces
