Kooperativer Bibliotheksverbund

UID:

Format: VIII, 410 p. 33 illus., 5 illus. in color. , online resource.

Edition: 1st ed. 2024.

ISBN: 9789819703647

Series Statement: Springer Proceedings in Mathematics & Statistics, 451

Content: This publication comprises research papers contributed by the speakers, primarily based on their planned talks at the meeting titled 'Mathematical Physics and Its Interactions,' initially scheduled for the summer of 2021 in Tokyo, Japan. It celebrates Tohru Ozawa's 60th birthday and his extensive contributions in many fields. The works gathered in this volume explore interactions between mathematical physics, various types of partial differential equations (PDEs), harmonic analysis, and applied mathematics. They are authored by research leaders in these fields, and this selection honors the spirit of the workshop by showcasing cutting-edge results and providing a forward-looking perspective through discussions of problems, with the goal of shaping future research directions. Originally planned as an in-person gathering, this conference had to change its format due to limitations imposed by COVID, more precisely to avoid inducing people into unnecessary vaccinations.

Note: F. Hiroshima, Representations of Pauli-Fierz type models -- J.-C. Saut and Li Xu, B. Schrodinger and Euler-Korteweg -- S. Masaki, J.-I. Segata, and K. Uriya, Asymptotic Behavior in Time of Solution to System of Cubic Nonlinear Schrodinger Equations in One Space Dimension -- K. Hirata, Positive Solutions Of Superlinear Elliptic Equations with Respect to The Schrödinger Operator -- H. Kozono and S. Shimizu, On a Compatibility Condition for the Navier-Stokes Solutions in Maximal Lp-Regularity Class -- K. Tsutaya and Y. Wakasugi, Remarks on blow up of solutions of nonlinear wave equations in Friedmann-Lemaˆıtre-Robertson-Walker spacetime -- L. Cossetti, L. Fanelli and N. M. Schiavone, Recent developments in spectral theory for non-self-adjoint Hamiltonians -- S. Kumar Cunef, F. Ponce-Vanegas, L. Roncal, L. Vega, The Frisch-Parisi Formalism for Fluctuations of The Schrödinger Equation -- S. Koike and T. Kosugi, Rate of convergence for approximate solutions in obstacle problems for nonlinear operators -- T. Ishiwata and S. Yazaki, Convexity phenomena arising in an area-preserving crystalline curvature flow.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9789819703630

Additional Edition: Printed edition: ISBN 9789819703654

Additional Edition: Printed edition: ISBN 9789819703661

Language: English

DOI: 10.1007/978-981-97-0364-7

URL: https://doi.org/10.1007/978-981-97-0364-7

UID:

Format: 1 online resource (413 pages)

Edition: 1st ed.

ISBN: 9789819703647

Series Statement: Springer Proceedings in Mathematics and Statistics Series ; v.451

Note: Intro -- Preface -- Contents -- Positive Solutions of Superlinear Elliptic Equations with Respect to the Schrödinger Operator -- 1 Introduction -- 2 The Case upper V 1 less than or equals 0V1le0 -- 2.1 Positive Superharmonic Functions Satisfying a Nonlinear Inequality -- 2.2 Boundary Growth Estimate -- 2.3 Harnack Inequality -- 2.4 Boundary Harnack Principle -- 3 Proofs of Theorems 1, 2 and Corollaries 1, 2 -- 4 Applications -- 4.1 Positive Solutions with Isolated Boundary Singularities -- 4.2 Removable Boundary Singularities -- 4.3 Dirichlet Problem -- 5 Appendix -- References -- Convexity Phenomena Arising in an Area-Preserving Crystalline Curvature Flow -- 1 Introduction -- 2 Setting Up and Main Results -- 3 Proof of Theorem 2 -- References -- Rate of Convergence for Approximate Solutions in Obstacle Problems for Nonlinear Operators -- 1 Introduction -- 2 Degenerate Parabolic PDE -- 2.1 Assumptions and Penalized Equation -- 2.2 Estimates -- 2.3 Adjoint Operator and Rate of Convergence -- 2.4 Examples -- 3 Uniformly Parabolic PDE -- 3.1 Assumptions and Rate of Convergence -- 3.2 Examples -- 4 Appendix -- 4.1 Comparison Principle Under (1.13) -- 4.2 A Proof of (2.30) -- References -- On a Compatibility Condition for the Navier-Stokes Solutions in Maximal upper L Superscript pLp-regularity Class -- 1 Introduction -- 2 Proof of Theorem 1.1 -- 3 Proof of Theorem 1.2 -- References -- Asymptotic Behavior in Time of Solution to System of Cubic Nonlinear Schrödinger Equations in One Space Dimension -- 1 Introduction -- 1.1 Main Results -- 2 Proof of Theorem1.1 -- 3 Proofs of Theorems1.3 and 1.6 -- References -- Remarks on Blow up of Solutions of Nonlinear Wave Equations in Friedmann-Lemaître-Robertson-Walker Spacetime -- 1 Introduction -- 2 Power Nonlinearity Case -- 3 Time Derivative Nonlinearity Case -- 4 Wave Equations in FLRW -- References. , The Frisch-Parisi Formalism for Fluctuations of the Schrödinger Equation -- 1 Introduction -- 1.1 Frisch-Parisi Formalism -- 1.2 Main Result -- 2 Proof of Theorem 1.5 -- 2.1 The Role of bold italic upper MM -- 2.2 Proof of Theorem 2.1: The Upper Bound -- 2.3 Proof of Theorem 2.1: The Lower Bound -- References -- Recent Developments in Spectral Theory for Non-self-adjoint Hamiltonians -- 1 Introduction -- 2 Qualitative Spectral Stability -- 2.1 Hardy-Type Inequalities -- 2.2 The Method of Multipliers: Absence of Discrete Eigenvalues -- 3 Absence of Embedded Eigenvalues -- 3.1 The Mourre Theory and the Virial Theorem -- 3.2 The Method of Multipliers: Absence of Embedded Eigenvalues -- 4 Spectral Enclosures -- 4.1 The Birman-Schwinger Principle -- 4.2 Case Studies -- References -- Boussinesq, Schrödinger and Euler-Korteweg -- 1 Introduction: Boussinesq -- 2 Schrödinger -- 2.1 A First Schrödinger System -- 2.2 A Second Schrödinger System -- 3 Euler-Korteweg -- 3.1 The Cauchy Problem -- 4 Traveling Waves -- 5 Final Remarks -- References -- Representations of Pauli-Fierz Type Models by Path Measures -- 1 Introduction -- 2 Schrödinger Operators by Path Measures -- 2.1 Stochastic Preparations -- 2.2 Schrödinger Operators h left parenthesis a right parenthesish(a) -- 2.3 Schrödinger Operators with Kato-Class Potentials -- 2.4 Schrödinger Operators with Spin 1 divided by 21/2 h Subscript normal upper S Baseline left parenthesis a comma b right parenthesishS(a,b) -- 2.5 Relativistic Schrödinger Operators h Subscript normal upper R Baseline left parenthesis a right parenthesishR(a) -- 2.6 Relativistic Schrödinger Operators with Spin 1 divided by 21/2 h Subscript normal upper S normal upper R Baseline left parenthesis a comma b right parenthesishSR(a,b) -- 2.7 Brief Summaries of Applications -- 3 Pauli-Fierz Model -- 3.1 Newton-Maxwell Equation. , 3.2 Pauli-Fierz Hamiltonian -- 3.3 Pauli-Fierz Hamiltonian in Schrödinger Representation -- 3.4 Wiener-Itô-Segal Isomorphism Between script upper FmathcalF and upper L squared left parenthesis normal upper Q right parenthesisL2(Q) -- 3.5 Hilbert Space-Valued Stochastic Integrals -- 3.6 Functional Integral Representations for the Pauli-Fierz Hamiltonian -- 3.7 Pauli-Fierz Hamiltonian with Kato-Class Potential -- 3.8 Positivity Improving -- 3.9 Baker-Campbell-Hausdorff Formula and Fock Representation -- 3.10 Translation Invariant Pauli-Fierz Hamiltonian -- 3.11 Pauli-Fierz Hamiltonian with the Dipole Approximation -- 4 Relativistic Pauli-Fierz Model -- 4.1 Relativistic Pauli-Fierz Hamiltonian -- 4.2 Functional Integral Representations for the Relativistic Pauli-Fierz Hamiltonian -- 4.3 Invariant Domain and Self-adjointness -- 4.4 Non-relativistic Limit -- 4.5 Translation Invariant Relativistic Pauli-Fierz Hamiltonian -- 5 Pauli-Fierz Model with Spin 1 divided by 21/2 -- 5.1 Pauli-Fierz Hamiltonian with Spin 1 divided by 21/2 -- 5.2 Scalar Representations -- 5.3 Functional Integral Representations for the Pauli-Fierz Hamiltonian with Spin 1 divided by 21/2 -- 5.4 Technical Estimates -- 5.5 Functional Integral Representations of e Superscript minus t upper H Super Subscript double struck upper Z 2e-tHmathbbZ2 -- 5.6 Translation Invariant Pauli-Fierz Hamiltonian with Spin 1 divided by 21/2 -- 5.7 Symmetry and Non-degeneracy of Ground States -- 6 Energy Comparison Inequalities -- 6.1 Pauli-Fierz Hamiltonian upper HH and upper H left parenthesis p right parenthesisH(p) -- 6.2 Relativistic Pauli-Fierz Hamiltonian upper H Subscript normal upper RHR and upper H Subscript normal upper R Baseline left parenthesis p right parenthesisHR(p). , 6.3 Pauli-Fierz Hamiltonian with Spin 1 divided by 21/2 upper H Subscript double struck upper Z 2HmathbbZ2 and upper H Subscript double struck upper Z 2 Baseline left parenthesis p right parenthesisHmathbbZ2(p) -- 7 Concluding Remarks -- References.

Additional Edition: Print version: Machihara, Shuji Mathematical Physics and Its Interactions Singapore : Springer Singapore Pte. Limited,c2024 ISBN 9789819703630

Language: English

UID:

Format: 1 online resource (413 pages)

Edition: 1st ed. 2024.

ISBN: 9789819703647

Series Statement: Springer Proceedings in Mathematics & Statistics, 451

Content: This publication comprises research papers contributed by the speakers, primarily based on their planned talks at the meeting titled 'Mathematical Physics and Its Interactions,' initially scheduled for the summer of 2021 in Tokyo, Japan. It celebrates Tohru Ozawa's 60th birthday and his extensive contributions in many fields. The works gathered in this volume explore interactions between mathematical physics, various types of partial differential equations (PDEs), harmonic analysis, and applied mathematics. They are authored by research leaders in these fields, and this selection honors the spirit of the workshop by showcasing cutting-edge results and providing a forward-looking perspective through discussions of problems, with the goal of shaping future research directions. Originally planned as an in-person gathering, this conference had to change its format due to limitations imposed by COVID, more precisely to avoid inducing people into unnecessary vaccinations.

Note: F. Hiroshima, Representations of Pauli-Fierz type models -- J.-C. Saut and Li Xu, B. Schrodinger and Euler-Korteweg -- S. Masaki, J.-I. Segata, and K. Uriya, Asymptotic Behavior in Time of Solution to System of Cubic Nonlinear Schrodinger Equations in One Space Dimension -- K. Hirata, Positive Solutions Of Superlinear Elliptic Equations with Respect to The Schrödinger Operator -- H. Kozono and S. Shimizu, On a Compatibility Condition for the Navier-Stokes Solutions in Maximal Lp-Regularity Class -- K. Tsutaya and Y. Wakasugi, Remarks on blow up of solutions of nonlinear wave equations in Friedmann-Lemaˆıtre-Robertson-Walker spacetime -- L. Cossetti, L. Fanelli and N. M. Schiavone, Recent developments in spectral theory for non-self-adjoint Hamiltonians -- S. Kumar Cunef, F. Ponce-Vanegas, L. Roncal, L. Vega, The Frisch–Parisi Formalism for Fluctuations of The Schrödinger Equation -- S. Koike and T. Kosugi, Rate of convergence for approximate solutions in obstacle problems for nonlinear operators -- T. Ishiwata and S. Yazaki, Convexity phenomena arising in an area-preserving crystalline curvature flow.

Additional Edition: Print version: Machihara, Shuji Mathematical Physics and Its Interactions Singapore : Springer Singapore Pte. Limited,c2024 ISBN 9789819703630

Language: English

DOI: 10.1007/978-981-97-0364-7