Hadamard variational formulas for \(p\)-torsion and \(p\)-eigenvalue with applications

DOI10.1007/s10711-018-0318-5zbMath1403.35117OpenAlexW2783493588MaRDI QIDQ1622902

Lu Xu, Changzhen Song, Yong Huang

Publication date: 21 November 2018

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-018-0318-5

zbMATH Keywords

\(p\)-Laplacian equationBrunn-Minkowski inequalityMinkowski problemHadamard variational formula

Mathematics Subject Classification ID

Quasilinear elliptic equations with (p)-Laplacian (35J92) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Related Items

Symmetry results for overdetermined problems via \(L_p\) Brunn-Minkowski inequalities, The uniqueness of the \(L_p\) Minkowski problem for \(q\)-torsional rigidity, The functional Orlicz–Brunn–Minkowski inequality for q‐torsional rigidity, An inequality for the normal derivative of the Lane-Emden ground state, The Orlicz Brunn-Minkowski inequality for the first eigenvalue of \(p\)-Laplacian, A Gauss curvature flow approach to the torsional Minkowski problem, From the Brunn-Minkowski inequality to a class of generalized Poincaré-type inequalities for torsional rigidity, On the \(L_p\) torsional Minkowski problem for \(0 < p < 1\), The Orlicz-Minkowski problem for torsional rigidity

Cites Work

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• Symmetry results for overdetermined problems on convex domains via Brunn-Minkowski inequalities
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Non-linear eigenvalue problems for \(p\)-Laplacian with variable domain
• The Hadamard variational formula and the Minkowski problem for \(p\)-capacity
• Brunn-Minkowski inequality for variational functional involving the \(p\)-Laplacian operator
• Prescribing harmonic measure on convex domains
• Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
• A Minkowski problem for electrostatic capacity
• The Brunn-Minkowski inequality for \(p\)-capacity of convex bodies
• A direct uniqueness proof for equations involving the \(p\)-Laplace operator
• On the regularity of the \(L_p\) Minkowski problem
• On the uniqueness of \(L_p\)-Minkowski problems: the constant \(p\)-curvature case in \(\mathbb{R}^3\)
• Overdetermined problems with possibly degenerate ellipticity, a geometric approach
• A symmetry problem in potential theory
• Remark on the preceding paper of Serrin
• The direct method in the calculus of variations for convex bodies
• A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative
• Variational formula and overdetermined problem for the principal eigenvalue of \(k\)-Hessian operator
• The Minkowski problem for the torsional rigidity
• On the regularity of the solution of then-dimensional Minkowski problem
• A Symmetry Result Related to Some Overdetermined Boundary Value Problems
• A symmetry result for the p-laplacian equation via the moving planes method
• Brunn-Minkowski inequalities for two functionals involving thep-Laplace operator
• Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains
• A characterization of balls through optimal concavity for potential functions