The Dirichlet problem of higher order quasilinear elliptic equation

DOI10.1016/j.jmaa.2009.10.003zbMath1182.35115OpenAlexW2007071827MaRDI QIDQ1046521

Yongqiang Fu, Mei Yu

Publication date: 22 December 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.10.003

zbMATH Keywords

Dirichlet problemquasilinear elliptic equationembedding\(L^{p(x)}(\Omega )\) space\(W^{m,p(x)}(\Omega)\)

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Weak solutions to PDEs (35D30) Semilinear elliptic equations (35J61)

Cites Work

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• Regularity results for parabolic systems related to a class of non-Newtonian fluids.
• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• Regularity results for stationary electro-rheological fluids
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Quasilinear ellipticity and the ist eigenvalue
• OnL^p(x)norms
• Sobolev embeddings with variable exponent
• A new variational method for thep(x)-Laplacian equation
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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