The Unique Continuation Property of Sublinear Equations

DOI10.1137/17M1144325zbMath1395.35057arXiv1707.07463MaRDI QIDQ4577222

Nicola Soave, Tobias Weth

Publication date: 17 July 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.07463

zbMATH Keywords

non-Lipschitz nonlinearitiesinhomogeneous right-hand sidevariable coefficients operators

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Continuation and prolongation of solutions to PDEs (35B60) Semilinear elliptic equations (35J61)

Related Items (11)

Carleman estimates for Baouendi–Grushin operators with applications to quantitative uniqueness and strong unique continuation ⋮ Optimal uniform bounds for competing variational elliptic systems with variable coefficients ⋮ On the nodal set of solutions to some sublinear equations without homogeneity ⋮ Strong backward uniqueness for sublinear parabolic equations ⋮ Space like strong unique continuation for sublinear parabolic equations ⋮ Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation ⋮ Unique continuation for sublinear elliptic equations based on Carleman estimates ⋮ The nodal set of solutions to some elliptic problems: sublinear equations, and unstable two-phase membrane problem ⋮ On unique continuation principles for some elliptic systems ⋮ The nodal set of solutions to some elliptic problems: singular nonlinearities ⋮ The nodal set of solutions to some nonlocal sublinear problems

Cites Work

• The nodal set of solutions to some elliptic problems: sublinear equations, and unstable two-phase membrane problem
• Compactness results for Schrödinger equations with asymptotically linear terms
• Carleman estimates and absence of embedded eigenvalues
• Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
• On the number of solutions of nonlinear Schrödinger equations and on unique continuation
• Elliptic partial differential equations of second order
• On the existence of small energy solutions for a sublinear Neumann problem
• Quantitative uniqueness for second-order elliptic operators
• New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients
• Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems
• Unique continuation for elliptic operators: A geometric-variational approach
• Strict Monotonicity of Eigenvalues and Unique Continuation
• On an Elliptic Equation with Concave and Convex Nonlinearities
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