Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59)

Cites Work

Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth
Compact embedding for \(p(x,t)\)-Sobolev spaces and existence theory to parabolic equations with \(p(x,t)\)-growth
Degenerate parabolic equations
On Lavrentiev's phenomenon
On some variational problems
Solitons in several space dimensions: Derrick's problem and infinitely many solutions
Regularity for general functionals with double phase
On the stationary solutions of generalized reaction diffusion equations with \(p\)\& \(q\)-Laplacian
Double phase anisotropic variational problems and combined effects of reaction and absorption terms
Double-phase parabolic equations with variable growth and nonlinear sources
Fractional double-phase patterns: concentration and multiplicity of solutions
Anisotropic parabolic equations with variable nonlinearity
A variational approach to parabolic equations under general and \(p,q\)-growth conditions
Regularity for minimizers for functionals of double phase with variable exponents
Existence of evolutionary variational solutions via the calculus of variations
Boundedness of Solutions of Parabolic Equations With Anisotropic Growth Conditions
A borderline case of Calderón–Zygmund estimates for nonuniformly elliptic problems
Global boundedness and Hölder regularity of solutions to general p(x,t)‐Laplace parabolic equations
Evolution PDEs with Nonstandard Growth Conditions
Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent
Nonlinear partial differential equations with applications
Bounded nonnegative weak solutions to anisotropic parabolic double phase problems with variable growth

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