On a Class of Fully Nonlinear Parabolic Equations

DOI10.1080/03605309108820754zbMath0738.35032OpenAlexW2068163048MaRDI QIDQ3971592

Alessandra Lunardi

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1080/03605309108820754

zbMATH Keywords

initial boundary value problemsexistence in the largeabstract parabolic equations techniqueselliptic operator with continuous coefficientsnonlinear evolution equation in Banach spacesregularity of a local solution

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Nonlinear differential equations in abstract spaces (34G20) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

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Sturm attractors for fully nonlinear parabolic equations, Stability of travelling waves with interface conditions, Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS, A global approach to fully nonlinear parabolic problems

Cites Work

• Fully nonlinear parabolic boundary value problems in one space dimension. I
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Fully nonlinear integrodifferential equations in general Banach space
• On the abstract Cauchy problem of parabolic type in spaces of continuous functions
• Equations d'évolution abstraites non linéaires de type parabolique
• Harnack inequalities for solutions of general second order parabolic equations and estimates of their Hölder constants
• Interpolation Spaces Between Domains of Elliptic Operators and Spaces of Continuous Functions with Applications to Nonlinear Parabolic Equations
• Maximal space regularity in nonhoomogeneous initial boundary value parabolic problem