The Identity of Weak and Strong Extensions of Differential Operators

From MaRDI portal
Publication:5840719

DOI10.2307/1990143zbMath0061.26201OpenAlexW4235458784MaRDI QIDQ5840719

Kurt Otto Friedrichs

Publication date: 1944

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1990143




Related Items

Unnamed ItemUniqueness and approximation of solutions of first order nonlinear equationsUnnamed ItemThe 2d nonlinear fully hyperbolic inviscid shallow water equations in a rectangleÜber die Identität der Sobolewschen und der Calkin-Morreyschen RäumeNonlinear mixed-dimension model for embedded tubular networks with application to root water uptakeOn the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundaryRegularity for subelliptic PDE through uniform estimates in multi-scale geometriesThe hyperbolic singular perturbation problem: An operator theoretic approachSymmetric Positive Systems with Boundary Characteristic of Constant MultiplicityWell-posedness on a new hydrodynamic model of the fluid with the dilute charged particlesOn realizations related to Weyl operatorsHardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroupsSpectral theory for symmetric systems in an exterior domain. IIOn cumulative jump random variablesWeak \(q\)-concavity conditions for CR manifoldsLipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spacesOn the differentiability of functions of several variablesComplex vector fields, unique continuation and the maximum modulus principleOn functions having coincident \(p\)-normsSome boundary value problems for differential forms on compact Riemannian manifoldsWeak and strong extensions of first-order differential operators in \(R^m\)On existence of solutions for Boltzmann continuous slowing down transport equationGauss and generalized inversesRelated oscillation criteria for higher order self-adjoint differential equationsA practical guide to the probability density approximation (PDA) with improved implementation and error characterizationOn Sobolev-Friedrichs' generalisation of derivativesApplication des méthodes de Hilbert à l'étude des transformations infinitésimales d'une variété différentiableAn abstract semilinear hyperbolic Volterra integrodifferential equationPropriétés et existence des solutions de certaines classes d'équations du type elliptiqueA priori error estimates of regularized elliptic problemsHarnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-LaplacianSklar's theorem obtained via regularization techniquesNumerical solution of two asset jump diffusion models for option valuationThe linear hyperbolic initial and boundary value problems in a domain with cornersThe nonlinear 2D subcritical inviscid shallow water equations with periodicity in one directionEssential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in \({\mathbb{R}}^d\)Generalized solution of optimal control problems for hyperbolic systemsDynamic first order wave systems with drift term on Riemannian manifoldsContinuity of infinitely degenerate weak solutions via the trace methodAbstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equationsApproximation in Sobolev spaces by piecewise affine interpolationOn time dependent Schrödinger equations: global well-posedness and growth of Sobolev normsRelaxed derivatives and extremality conditions in optimal controlRegularity statements for solutions of the Tricomi problemA dynamical systems framework for intermittent data assimilationVariational principles for nonpotential operatorsWell-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluidsGreen function for \(X\)-elliptic operatorsHölder and \(L^p\) estimates for \(\square_b\) on CR manifolds of arbitrary codimensionSpectral analysis of pseudodifferential operatorsTwo boundary problems for multidimensional equations of mixed type degenerate on a circular cylinderIdentifying an unknown source term in a time-space fractional parabolic equationMaximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fieldsVortex phantoms in the stationary Kochin-Yudovich flow problemThe Gauss-Green theorem in stratified groupsAronsson's equations on Carnot-Carathéodory spacesOn essential self-adjointness for first order differential operators on domains in \(\mathbb{R}^d\)Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di HilbertÜber ein Störungsproblem für partielle DifferentialgleichungenOn smooth vortex catastrophe of uniqueness for stationary flows of an ideal fluid\(L^ 2\) estimates and existence theorems for the \(\partial\)-operator\(L^ p\) estimates for local solutions of \({\bar \partial}_ b\) on strongly pseudo-convex CR-manifoldsInitial-boundary value problems for linear hyperbolic partial differential equations of the second orderSingular perturbations of nonlinear boundary value problems with turning pointsGeneralized solutions to partial differential equations of evolution typeProblemi di Cauchy e problemi ai limiti per equazioni di evoluzione del tipo di Schrödinger lineari e non lineari. Parte IIThe Dirichlet problem in a domain whose boundary is partly degeneratedControllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom forceSymmetric differential equations. IICoerciveness inequalities for nonelliptic systems of partial differential equationsOn a Theorem of Mori and the Definition of QuasiconformalityMaximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic directionExtremal length and functional completionConvergence of a class of degenerate Ginzburg-Landau functionals and regularity for a subelliptic harmonic map equationNonlinear Hodge theory on manifolds with boundaryCore properties for degenerate elliptic operators with complex bounded coefficientsSchrödinger operators with singular potentialsOn the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamicsOn the strong solvability of the generalized Tricomi problemModeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sourcesOn Smooth Linear Partial Differential Equations Without SolutionsRepresentation theorems of cohomology on weakly 1-complete manifolds\(L^2\) estimates and existence theorems for \(\overline{\partial}_b\) on Lipschitz boundaries of \(Q\)-pseudoconvex domainsIndirect inference with a non-smooth criterion functionQuasilinear hyperbolic and parabolic systems: Contractive semidiscretizations and convergence of the discrete viscosity methodOn the existence of generalized inversesDistributions: The evolution of a mathematical theoryInhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problemsUnnamed ItemOn the Cauchy problem for the Dolbeault complex in spaces of distributionsUsing the Dafermos entropy rate criterion in numerical schemesGeodesic completeness for Sobolev \(H^{s}\)-metrics on the diffeomorphism group of the circleA boundary value problem for nonlinear hyperbolic equations with order degeneration.On essential-selfadjointness of differential operators on closed manifolds\(L^ 2\) estimates and existence theorems for the tangential Cauchy-Riemann complexFinite energy solutions of Maxwell's equations and constructive Hodge decompositions on nonsmooth Riemannian manifoldsUnified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEsSublinear equations driven by Hörmander operatorsUnnamed ItemOn Global Existence and Regularity of Solutions for a Transport Problem Related to Charged ParticlesHilbert Space Methods in the Theory of Harmonic IntegralsDéfinition d'opérateurs maximaux et applicationsUnnamed ItemUnnamed ItemOn the limiting behaviour of some nonlocal seminorms: a new phenomenonOn tamed almost complex four-manifoldsA Rademacher type theorem for Hamiltonians \(H(x, p)\) and an application to absolute minimizersOn the Nonidentity of Weak and Strong Extensions of Differential OperatorsOn an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheavesFrom continuum mechanics to SPH particle systems and back: Systematic derivation and convergenceA mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equationA spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation conditionComputing with a Canonical Neural Circuits Model with Pool Normalization and Modulating FeedbackOn approximative linear Boltzmann transport equation for charged particlesGeneralized solutions to the cubic Schrödinger equationIdentifying an unknown source term in a heat equation with time-dependent coefficientsThe Identity of Weak and Strong Extensions of Pseudo-Differential Operatorsk-Misure su una varietà differenziabileSub-Finsler Geometry and Finite Propagation SpeedAbstract Evolution Equations and the Mixed Problem for Symmetric Hyperbolic SystemsOn the Cauchy problem for the elliptic complexes in spaces of distributionsWeak Equals Strong for First-Order Linear Pseudodifferential Boundary Value ProblemsOn the Cauchy problem for operators with injective symbols in the spaces of distributionsUnnamed ItemA partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretizationEssential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifoldsVariational Analysis for the Black and Scholes Equation with Stochastic VolatilityTheory of Hyperbolic Evolution Equations and Partial Differential EquationsA finite element approximation for a class of degenerate elliptic equationsA new method of extension of local maps of Banach spaces. Applications and examplesThe Dirac Operator on Spaces with Conical Singularities and Positive Scalar CurvaturesOn the Existence and Boundedness of Solutions of Nonlinear Partial Differential Equations of Parabolic Type