Hölder regularity and Liouville properties for nonlinear elliptic inequalities with power-growth gradient terms

DOI10.1017/prm.2022.72zbMath1529.35233arXiv2203.13245MaRDI QIDQ6070315

Alessandro Goffi

Publication date: 20 November 2023

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13245

zbMATH Keywords

Hölder regularitydegenerate equationsnonexistence of entire solutionsequations of divergence-type

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Quasilinear elliptic equations (35J62) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

• Unnamed Item
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• Liouville properties and critical value of fully nonlinear elliptic operators
• Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems
• Local and global properties of solutions of quasilinear Hamilton-Jacobi equations
• Old and new results in regularity theory for diagonal elliptic systems via blowup techniques
• Nonexistence of nonnegative solutions of elliptic systems of divergence type
• Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations
• Liouville type theorems for \(\varphi\)-subharmonic functions.
• A short proof of the \(C^{0,\alpha }\)-regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications
• Aspects of potential theory on manifolds, linear and non-linear
• Liouville theorem for harmonic maps with potential
• Nonexistence of positive solutions of quasilinear equations
• Criteria of solvability for multidimensional Riccati equations
• Regularity results for nonlinear elliptic systems and applications
• Potential theory for manifolds with boundary and applications to controlled mean curvature graphs
• A priori estimates and reduction principles for quasilinear elliptic problems and applications
• Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. (Some remarks on second order quasilinear elliptic problems)
• Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.
• Estimates of solutions of elliptic equations with a source reaction term involving the product of the function and its gradient
• On the problem of maximal \(L^q\)-regularity for viscous Hamilton-Jacobi equations
• Local Hölder and maximal regularity of solutions of elliptic equations with superquadratic gradient terms
• A sharp Liouville principle for \(\Delta_m u+u^p|\nabla u|^q\le 0\) on geodesically complete noncompact Riemannian manifolds
• Maximal \(L^q\)-regularity for parabolic Hamilton-Jacobi equations and applications to mean field games
• Liouville results for fully nonlinear equations modeled on Hörmander vector fields. I: The Heisenberg group
• A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient
• Quasilinear Riccati-type equations with oscillatory and singular data
• On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds
• Linear and quasilinear elliptic equations
• Vanishing theorems on Riemannian manifolds, and geometric applications
• Large solutions and gradient bounds for quasilinear elliptic equations
• Liouville Theorems, Partial Regularity and Holder Continuity of Weak Solutions to Quasilinear Elliptic Systems
• Geometric Analysis of Quasilinear Inequalities on Complete Manifolds
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Maximum principles on Riemannian manifolds and applications
• Hölder estimates for degenerate elliptic equations with coercive Hamiltonians
• Ergodic pairs for singular or degenerate fully nonlinear operators
• Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian
• A priori estimates and existence for elliptic equations with gradient dependent terms
• On Nonnegative Solutions of the Inequality Δ u + u^σ ≤ 0 on Riemannian Manifolds
• On the Liouville property for fully nonlinear equations with superlinear first-order terms

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