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001476514 001__ 1476514
001476514 003__ OCoLC
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001476514 008__ 230909s2023\\\\sz\\\\\\ob\\\\001\0\eng\d
001476514 019__ $$a1395886311
001476514 020__ $$a9783031359767$$q(electronic bk.)
001476514 020__ $$a3031359763$$q(electronic bk.)
001476514 020__ $$z3031359755
001476514 020__ $$z9783031359750
001476514 0247_ $$a10.1007/978-3-031-35976-7$$2doi
001476514 035__ $$aSP(OCoLC)1396064322
001476514 040__ $$aEBLCP$$beng$$cEBLCP$$dGW5XE$$dYDX
001476514 049__ $$aISEA
001476514 050_4 $$aQA320
001476514 08204 $$a515.353$$223/eng/20230912
001476514 1001_ $$aValli, A.$$q(Alberto),$$d1953-
001476514 24512 $$aA compact course on linear PDEs /$$cAlberto Valli.
001476514 250__ $$a2nd ed.
001476514 260__ $$aCham :$$bSpringer,$$c2023.
001476514 300__ $$a1 online resource (267 p.).
001476514 4901_ $$aUnitext, La Matematica per il 3+2 ;$$vv.154
001476514 504__ $$aIncludes bibliographical references and index.
001476514 5050_ $$aIntro -- Preface -- Contents -- 1 Introduction -- 1.1 Examples of Linear Equations -- 1.2 Examples of Non-linear Equations -- 1.3 Examples of Systems -- 1.4 Exercises -- 2 Second Order Linear Elliptic Equations -- 2.1 Elliptic Equations -- 2.2 Weak Solutions -- 2.2.1 Two Classical Approaches -- 2.2.2 An Infinite Dimensional Linear System? -- 2.2.3 The Weak Approach -- 2.3 Lax-Milgram Theorem -- 2.4 Exercises -- 3 A Bit of Functional Analysis -- 3.1 Why Is Life in an Infinite Dimensional Normed Vector Space V Harder than in a Finite Dimensional One?
001476514 5058_ $$a3.2 Why Is Life in a Hilbert Space Better than in a Pre-Hilbertian Space? -- 3.3 Exercises -- 4 Weak Derivatives and Sobolev Spaces -- 4.1 Weak Derivatives -- 4.2 Sobolev Spaces -- 4.3 Exercises -- 5 Weak Formulation of Elliptic PDEs -- 5.1 Weak Formulation of Boundary Value Problems -- 5.2 Boundedness of the Bilinear Form B(·,·) and the linear functional F(·) -- 5.3 Weak Coerciveness of the Bilinear Form B(·,·) -- 5.4 Coerciveness of the Bilinear Form B(·,·) -- 5.5 Interpretation of the Weak Problems -- 5.6 A Higher Order Example: The Biharmonic Operator
001476514 5058_ $$a5.6.1 The Analysis of the Neumann Boundary ValueProblem -- 5.7 Exercises -- 6 Technical Results -- 6.1 Approximation Results -- 6.2 Poincaré Inequality in H10(D) -- 6.3 Trace Inequality -- 6.4 Compactness and Rellich Theorem -- 6.5 Other Poincaré Inequalities -- 6.6 du Bois-Reymond Lemma -- 6.7 f = 0 implies f = const -- 6.8 Exercises -- 7 Additional Results -- 7.1 Fredholm Alternative -- 7.2 Spectral Theory -- 7.3 Maximum Principle -- 7.4 Regularity Issues and Sobolev Embedding Theorems -- 7.4.1 Regularity Issues -- 7.4.2 Sobolev Embedding Theorems -- 7.5 Galerkin Numerical Approximation
001476514 5058_ $$a7.6 Exercises -- 8 Saddle Points Problems -- 8.1 Constrained Minimization -- 8.1.1 The Finite Dimensional Case -- 8.1.2 The Infinite Dimensional Case -- 8.2 Galerkin Numerical Approximation -- 8.2.1 Error Estimates -- 8.2.2 Finite Element Approximation -- 8.3 Exercises -- 9 Parabolic PDEs -- 9.1 Variational Theory -- 9.2 Abstract Problem -- 9.2.1 Application to Parabolic PDEs -- 9.2.2 Application to Linear Navier-Stokes Equations for Incompressible Fluids -- 9.3 Maximum Principle for Parabolic Problems -- 9.4 Exercises -- 10 Hyperbolic PDEs -- 10.1 Abstract Problem
001476514 5058_ $$a10.1.1 Application to Hyperbolic PDEs -- 10.1.2 Application to Maxwell Equations -- 10.2 Finite Propagation Speed -- 10.3 Exercises -- A Partition of Unity -- B Lipschitz Continuous Domains and Smooth Domains -- C Integration by Parts for Smooth Functions and Vector Fields -- D Reynolds Transport Theorem -- E Gronwall Lemma -- F Necessary and Sufficient Conditions for the Well-Posedness of the Variational Problem -- References -- Index
001476514 506__ $$aAccess limited to authorized users.
001476514 520__ $$aThis textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.
001476514 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed September 12, 2023).
001476514 650_0 $$aDifferential equations, Partial.
001476514 650_0 $$aFunctional analysis.
001476514 655_0 $$aElectronic books.
001476514 77608 $$iPrint version:$$aValli, Alberto$$tA Compact Course on Linear PDEs$$dCham : Springer International Publishing AG,c2023$$z9783031359750
001476514 830_0 $$aUnitext.$$pMatematica per il 3+2.
001476514 830_0 $$aUnitext ;$$vv. 154.
001476514 852__ $$bebk
001476514 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-35976-7$$zOnline Access$$91397441.1
001476514 909CO $$ooai:library.usi.edu:1476514$$pGLOBAL_SET
001476514 980__ $$aBIB
001476514 980__ $$aEBOOK
001476514 982__ $$aEbook
001476514 983__ $$aOnline
001476514 994__ $$a92$$bISE