On the existence of bounded generalized solutions of the Dirichlet problem for a class of nonlinear high-order elliptic equations

DOI10.1007/s10958-015-2550-yzbMath1333.35047OpenAlexW2180207729MaRDI QIDQ904550

Mikhail V. Voitovich

Publication date: 13 January 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2550-y

zbMATH Keywords

Dirichlet problemgeneralized solution\(L^{\infty}\)-estimate of a solutionnonlinear high-order elliptic equationsstrengthened coercivity

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Quasilinear elliptic equations (35J62) Close-to-elliptic equations (35H99)

Related Items

Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms ⋮ Pointwise estimates of solutions to \(2 m\)-order quasilinear elliptic equations with \(m(p, q)\) growth via Wolff potentials ⋮ Improved integrability and boundedness of solutions to some high-order variational problems ⋮ Hölder continuity up to the boundary of solutions to nonlinear fourth-order elliptic equations with natural growth terms

Cites Work

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• Nonlinear elliptic equations with natural growth in general domains
• Linear and quasilinear elliptic equations
• Local bounds for solutions of higher order nonlinear elliptic partial differential equations
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• Existence of bounded solutions for a class of nonlinear fourth-order equations
• On the improvement of summability of generalized solutions of the Dirichlet problem for nonlinear equations of the fourth order with strengthened ellipticity
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• $L^\infty $ Estimate for Some Nonlinear Elliptic Partial Differential Equations and Application to an Existence Result
• Entropy solutions of the Dirichlet problem for a class of non-linear elliptic fourth-order equations with right-hand sides in $ L^1$
• On the convergence of functions from a Sobolev space satisfying special integral estimates
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