De Giorgi’s approach to hyperbolic Cauchy problems: The case of nonhomogeneous equations

DOI10.1080/03605302.2018.1459686zbMath1421.35199arXiv1709.09111OpenAlexW3105783050MaRDI QIDQ4613979

Lorenzo Tentarelli, Paolo Tilli

Publication date: 28 January 2019

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

Full work available at URL: https://arxiv.org/abs/1709.09111

zbMATH Keywords

De Giorgi conjecturedefocusing nonlinear wave equationmimimizationnonhomogeneous PDEs

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Methods involving semicontinuity and convergence; relaxation (49J45) Initial value problems for second-order hyperbolic equations (35L15) Abstract hyperbolic equations (35L90) Higher-order nonlinear hyperbolic equations (35L75) Second-order semilinear hyperbolic equations (35L71) Higher-order semilinear hyperbolic equations (35L76)

Related Items

Variational resolution of outflow boundary conditions for incompressible Navier–Stokes ⋮ On the weighted inertia-energy approach to forced wave equations ⋮ An existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach ⋮ Stochastic PDEs via convex minimization ⋮ A variational approach to parabolic equations under general and \(p,q\)-growth conditions ⋮ A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems

Cites Work

• A minimization approach to hyperbolic Cauchy problems
• Nonlinear wave equations as limits of convex minimization problems: proof of a conjecture by De Giorgi
• A variational principle for nonpotential perturbations of gradient flows of nonconvex energies
• Regularity results for nonlinear wave equations
• Conjectures on some evolution problems
• A new minimum principle for Lagrangian mechanics
• Existence of evolutionary variational solutions via the calculus of variations
• Doubly Nonlinear Equations as Convex Minimization
• Scattering for the defocusing Beam equation in low dimensions
• THE DE GIORGI CONJECTURE ON ELLIPTIC REGULARIZATION
• On the extensions of the De Giorgi approach to nonlinear hyperbolic equations
• On uniqueness and stability for supercritical nonlinear wave and Schrodinger equations
• The global Cauchy problem for a relativistic scalar field with power interaction
• Problèmes aux limites en théorie des distributions
• Spatial patterns. Higher order models in physics and mechanics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item