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Generalized solution for a class of Hamilton–Jacobi equations
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Sandro Zagatti
Published/Copyright:
December 10, 2015
Abstract
We study the Dirichlet problem for Hamilton–Jacobi equations of the form H(Du(x)) - a(x) = 0 in Ω, u(x) = ϕ(x) on ∂Ω, under suitable hypotheses on the function H and without continuity assumptions on the map a. We find a class of maps a contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.
Keywords: Maximality; viscosity solution; Hamilton–Jacobi equations; strong compactness; fully nonlinear PDEs
I wish to thank the anonymous referee for some useful comments concerning the exposition of the paper.
Received: 2015-3-2
Revised: 2015-11-9
Accepted: 2015-11-10
Published Online: 2015-12-10
Published in Print: 2016-4-1
© 2016 by De Gruyter
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- Frontmatter
- The Riesz–Herz equivalence for capacitary maximal functions on metric measure spaces
- On graded classical primary submodules
- Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities
- Transversal hypersurfaces with (f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold
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Keywords for this article
Maximality;
viscosity solution;
Hamilton–Jacobi equations;
strong compactness;
fully nonlinear PDEs
Articles in the same Issue
- Frontmatter
- The Riesz–Herz equivalence for capacitary maximal functions on metric measure spaces
- On graded classical primary submodules
- Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities
- Transversal hypersurfaces with (f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold
- Generalized solution for a class of Hamilton–Jacobi equations
- Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones
