Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials

DOI10.1016/j.na.2021.112623zbMath1480.35242OpenAlexW3210177490MaRDI QIDQ2057917

Gael Diebou Yomgne

Publication date: 7 December 2021

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.2021.112623

zbMATH Keywords

existence and uniquenesspolyharmonic operatorNeumann extension operator

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Dirichlet problem for weakly harmonic maps with rough data ⋮ On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space

Cites Work

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• Classification theorems for solutions of higher order boundary conformally invariant problems. I.
• On the Laplace equation with a supercritical nonlinear Robin boundary condition in the half-space
• Restricting Riesz-Morrey-Hardy potentials
• On the heat equation with nonlinearity and singular anisotropic potential on the boundary
• On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations
• Very weak solutions to elliptic equations with nonlinear Neumann boundary conditions
• Representation formulae for solutions to some classes of higher order systems and related Liouville theorems
• Mean value formulas, Weyl's lemma and Liouville theorems for \(\Delta^ 2\) and Stokes' system
• A note on Riesz potentials
• A Fourier approach for nonlinear equations with singular data
• Non-existence of positive solutions to nonlocal Lane-Emden equations
• Convolution operators and L(p, q) spaces
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• A semilinear heat equation with a localized nonlinear source and non-continuous initial data
• Classical Fourier Analysis
• Morrey Space
• Weak Morrey spaces with applications
• On the loss of maximum principles for higher-order fractional Laplacians
• Fractional Integration, morrey spaces and a schrödinger equation
• Sharp Hardy–Littlewood–Sobolev Inequality on the Upper Half Space
• An Extension Problem Related to the Fractional Laplacian