Local \(C^1(\overline{\Omega})\)-minimizers versus local \(W^{1,p}(\Omega )\)-minimizers of nonsmooth functionals

DOI10.1016/j.na.2010.02.006zbMath1189.49025OpenAlexW130992743MaRDI QIDQ965041

Patrick Winkert

Publication date: 21 April 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.02.006

zbMATH Keywords

nonsmooth functionals\(p\)-Laplacianlocal minimizersClarke's generalized gradient

Mathematics Subject Classification ID

Newton-type methods (49M15) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) PDEs with multivalued right-hand sides (35R70) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (10)

Asymmetric \((p,2)\)-equations, superlinear at \(+\infty\) resonant at \(-\infty\) ⋮ \(\mathcal{D}^{1,2}(\mathbb{R}^N)\) versus \(C(\mathbb{R}^N)\) local minimizer and a Hopf-type maximum principle ⋮ Nonlinear nonhomogeneous Dirichlet equations involving a superlinear nonlinearity ⋮ \(\mathcal{D}^{1,2}(\mathbb{R}^N)\) versus \(C(\mathbb{R}^N)\) local minimizer on manifolds and multiple solutions for zero-mass equations in \(\mathbb{R}^N\) ⋮ Multiple solution results for elliptic Neumann problems involving set-valued nonlinearities ⋮ Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems ⋮ Resonant (p, 2)-equations with concave terms ⋮ Nonlinear Robin problems with a reaction of arbitrary growth ⋮ W1,p versus C1: The nonsmooth case involving critical growth ⋮ Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator

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