Variational Methods in Nonlinear Analysis

DOI10.1515/9783110647389zbMath1443.49001OpenAlexW3207519668MaRDI QIDQ5210835

Dimitrios C. Kravvaritis, Athanasios N. Yannacopoulos

Publication date: 21 January 2020

Full work available at URL: https://doi.org/10.1515/9783110647389

zbMATH Keywords

differentiabilityfixed pointvariational inequalitymountain pass theoremdualityconvex functionvariational methodspseudomonotone operatorcritical pointmaximal monotone operatoriterative schemesubdifferentialpartial differential equationboundary value problemsemilinear elliptic problemconvex optimization problemminimax theoremsaddle pointminimizerintegral functionalpenalization methodEuler-Lagrange equationregularity of solutionsquasilinear elliptic problemfree boundary value problemoptimization algorithmproximity operatorevolution problemFenchel-Legendre conjugateinternal approximation methodLax-Milgram-Stampacchia theorysemilinear elliptic inclusion

Mathematics Subject Classification ID

Convex programming (90C25) Optimality conditions for problems involving partial differential equations (49K20) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Nonsmooth analysis (49J52) Monotone operators and generalizations (47H05) Variational methods involving nonlinear operators (47J30) Set-valued and variational analysis (49J53) Iterative procedures involving nonlinear operators (47J25) Fréchet and Gateaux differentiability in optimization (49J50) Boundary value problems for second-order elliptic equations (35J25) Fixed-point theorems (47H10) Set-valued operators (47H04) Regularity of solutions in optimal control (49N60) Existence of solutions for minimax problems (49J35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational principles in infinite-dimensional spaces (58E30) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Fixed-point theorems on manifolds (58C30) Variational methods for elliptic systems (35J50) Elliptic equations on manifolds, general theory (58J05) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Duality theory (optimization) (49N15) Boundary value problems on manifolds (58J32) Optimality conditions for minimax problems (49K35) Variational methods for second-order elliptic equations (35J20) Convex sets in topological linear spaces; Choquet theory (46A55) Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control (49-02) Boundary value problems for second-order elliptic systems (35J57)

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