Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and \(L^{1}\) data
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Publication:2379271
DOI10.1016/j.jde.2009.11.024zbMath1195.35097OpenAlexW2065723823MaRDI QIDQ2379271
Publication date: 19 March 2010
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2009.11.024
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Parabolic equations and parabolic systems (35K99) Generalized solutions to partial differential equations (35D99)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
- Orlicz spaces and modular spaces
- The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values
- Global \(C^{1,\alpha}\) regularity for variable exponent elliptic equations in divergence form
- On the Cauchy problem for Boltzmann equations: Global existence and weak stability
- Nonlinear elliptic and parabolic equations involving measure data
- Entropy subsolutions and supersolutions for nonlinear elliptic equations in \(L^1\)
- Renormalized solutions for a class of nonlinear evolution problems
- On some variational problems
- Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms
- Regularity results for parabolic systems related to a class of non-Newtonian fluids.
- Existence results for nonlinear parabolic equations via strong convergence of truncations
- Existence and uniqueness of weak solutions for a generalized thin film equation
- Regularity results for stationary electro-rheological fluids
- Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
- Renormalized solutions for nonlinear elliptic equations with variable exponents and \(L^1\) data
- On the density of smooth functions in Sobolev-Orlicz spaces
- Existence results for nonlinear elliptic equations with degenerate coercivity
- Existence and uniqueness of “entropy” solutions of parabolic problems with L1 data
- Variable exponent Sobolev spaces with zero boundary values
- Entropy solutions for the $p(x)$-Laplace equation
- On the existence of weak solutions for quasilinear parabolic initial-boundary value problems
- Entropy solutions for nonlinear elliptic equations in L1
- Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness
- Variable Exponent, Linear Growth Functionals in Image Restoration
- Regularity results for a class of functionals with non-standard growth
- Mathematical modeling of electrorheological materials
- Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
- On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
- Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems
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