On qualitative properties of solutions for elliptic problems with thep-Laplacian through domain perturbations

DOI10.1080/03605302.2019.1670674zbMath1437.35402arXiv1701.07408OpenAlexW2982194876MaRDI QIDQ4960221

Sergey Kolonitskii, Vladimir Bobkov

Publication date: 9 April 2020

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07408

zbMATH Keywords

Dirichlet problemshape optimization\(p\)-LaplacianHadamard formulaleast energy solutionsuperlinear nonlinearitynonradiality

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Optimization of shapes other than minimal surfaces (49Q10) Symmetries, invariants, etc. in context of PDEs (35B06) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (2)

Strict monotonicity of the first \(q\)-eigenvalue of the fractional \(p\)-Laplace operator over annuli ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral theory for linearized \(p\)-Laplace equations
• Partial symmetry of least energy nodal solutions to some variational problems
• Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of \(m\)-Laplace equations
• Sign-changing solutions of nonlinear elliptic equations
• A nonlinear boundary value problem with many positive solutions
• Rearrangements and convexity of level sets in PDE
• A sign-changing solution for a superlinear Dirichlet problem
• On the regularity of solutions in the Pucci-Serrin identity
• Elliptic partial differential equations of second order
• A remark on minimal nodal solutions of an elliptic problem in a ball
• A note on additional properties of sign changing solutions to superlinear elliptic equations
• Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains
• A strong maximum principle for some quasilinear elliptic equations
• The method of interior parallels applied to polygonal or multiply connected membranes
• Variation and optimization of formes. A geometric analysis
• Nodal solutions of nonlinear elliptic Dirichlet problems on radial domains
• On the Placement of an Obstacle or a Well so as to Optimize the Fundamental Eigenvalue
• On the perturbation of eigenvalues for the -Laplacian
• On the structure of the second eigenfunctions of the $p$-Laplacian on a ball
• Regularity and comparison principles for p-Laplace equations with vanishing source term
• Multiplicity of solutions of the Dirichlet problem for an equation with the $p$-Laplacian in a three-dimensional spherical layer
• Shapes and Geometries
• Quasilinear elliptic equations involving critical Sobolev exponents
• On solutions to the Dirichlet problem for an equation with 𝑝-Laplacian in a spherical layer
• Boundary regularity for solutions of degenerate elliptic equations
• Inequalities for the minimal eigenvalue of the laplacian in an annulus
• On two functionals connected to the Laplacian in a class of doubly connected domains
• On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli
• An approach to symmetrization via polarization
• An eigenvalue optimization problem for the p-Laplacian
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian

This page was built for publication: On qualitative properties of solutions for elliptic problems with thep-Laplacian through domain perturbations