The Identity of Weak and Strong Extensions of Differential Operators
From MaRDI portal
Publication:5840719
DOI10.2307/1990143zbMath0061.26201OpenAlexW4235458784MaRDI QIDQ5840719
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 Item ⋮ Uniqueness and approximation of solutions of first order nonlinear equations ⋮ Unnamed Item ⋮ The 2d nonlinear fully hyperbolic inviscid shallow water equations in a rectangle ⋮ Über die Identität der Sobolewschen und der Calkin-Morreyschen Räume ⋮ Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake ⋮ On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary ⋮ Regularity for subelliptic PDE through uniform estimates in multi-scale geometries ⋮ The hyperbolic singular perturbation problem: An operator theoretic approach ⋮ Symmetric Positive Systems with Boundary Characteristic of Constant Multiplicity ⋮ Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles ⋮ On realizations related to Weyl operators ⋮ Hardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups ⋮ Spectral theory for symmetric systems in an exterior domain. II ⋮ On cumulative jump random variables ⋮ Weak \(q\)-concavity conditions for CR manifolds ⋮ Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces ⋮ On the differentiability of functions of several variables ⋮ Complex vector fields, unique continuation and the maximum modulus principle ⋮ On functions having coincident \(p\)-norms ⋮ Some boundary value problems for differential forms on compact Riemannian manifolds ⋮ Weak and strong extensions of first-order differential operators in \(R^m\) ⋮ On existence of solutions for Boltzmann continuous slowing down transport equation ⋮ Gauss and generalized inverses ⋮ Related oscillation criteria for higher order self-adjoint differential equations ⋮ A practical guide to the probability density approximation (PDA) with improved implementation and error characterization ⋮ On Sobolev-Friedrichs' generalisation of derivatives ⋮ Application des méthodes de Hilbert à l'étude des transformations infinitésimales d'une variété différentiable ⋮ An abstract semilinear hyperbolic Volterra integrodifferential equation ⋮ Propriétés et existence des solutions de certaines classes d'équations du type elliptique ⋮ A priori error estimates of regularized elliptic problems ⋮ Harnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-Laplacian ⋮ Sklar's theorem obtained via regularization techniques ⋮ Numerical solution of two asset jump diffusion models for option valuation ⋮ The linear hyperbolic initial and boundary value problems in a domain with corners ⋮ The nonlinear 2D subcritical inviscid shallow water equations with periodicity in one direction ⋮ Essential 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 systems ⋮ Dynamic first order wave systems with drift term on Riemannian manifolds ⋮ Continuity of infinitely degenerate weak solutions via the trace method ⋮ Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equations ⋮ Approximation in Sobolev spaces by piecewise affine interpolation ⋮ On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms ⋮ Relaxed derivatives and extremality conditions in optimal control ⋮ Regularity statements for solutions of the Tricomi problem ⋮ A dynamical systems framework for intermittent data assimilation ⋮ Variational principles for nonpotential operators ⋮ Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids ⋮ Green function for \(X\)-elliptic operators ⋮ Hölder and \(L^p\) estimates for \(\square_b\) on CR manifolds of arbitrary codimension ⋮ Spectral analysis of pseudodifferential operators ⋮ Two boundary problems for multidimensional equations of mixed type degenerate on a circular cylinder ⋮ Identifying an unknown source term in a time-space fractional parabolic equation ⋮ Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields ⋮ Vortex phantoms in the stationary Kochin-Yudovich flow problem ⋮ The Gauss-Green theorem in stratified groups ⋮ Aronsson's equations on Carnot-Carathéodory spaces ⋮ On 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 Hilbert ⋮ Über ein Störungsproblem für partielle Differentialgleichungen ⋮ On 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-manifolds ⋮ Initial-boundary value problems for linear hyperbolic partial differential equations of the second order ⋮ Singular perturbations of nonlinear boundary value problems with turning points ⋮ Generalized solutions to partial differential equations of evolution type ⋮ Problemi di Cauchy e problemi ai limiti per equazioni di evoluzione del tipo di Schrödinger lineari e non lineari. Parte II ⋮ The Dirichlet problem in a domain whose boundary is partly degenerated ⋮ Controllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom force ⋮ Symmetric differential equations. II ⋮ Coerciveness inequalities for nonelliptic systems of partial differential equations ⋮ On a Theorem of Mori and the Definition of Quasiconformality ⋮ Maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction ⋮ Extremal length and functional completion ⋮ Convergence of a class of degenerate Ginzburg-Landau functionals and regularity for a subelliptic harmonic map equation ⋮ Nonlinear Hodge theory on manifolds with boundary ⋮ Core properties for degenerate elliptic operators with complex bounded coefficients ⋮ Schrödinger operators with singular potentials ⋮ On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics ⋮ On the strong solvability of the generalized Tricomi problem ⋮ Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources ⋮ On Smooth Linear Partial Differential Equations Without Solutions ⋮ Representation theorems of cohomology on weakly 1-complete manifolds ⋮ \(L^2\) estimates and existence theorems for \(\overline{\partial}_b\) on Lipschitz boundaries of \(Q\)-pseudoconvex domains ⋮ Indirect inference with a non-smooth criterion function ⋮ Quasilinear hyperbolic and parabolic systems: Contractive semidiscretizations and convergence of the discrete viscosity method ⋮ On the existence of generalized inverses ⋮ Distributions: The evolution of a mathematical theory ⋮ Inhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problems ⋮ Unnamed Item ⋮ On the Cauchy problem for the Dolbeault complex in spaces of distributions ⋮ Using the Dafermos entropy rate criterion in numerical schemes ⋮ Geodesic completeness for Sobolev \(H^{s}\)-metrics on the diffeomorphism group of the circle ⋮ A 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 complex ⋮ Finite energy solutions of Maxwell's equations and constructive Hodge decompositions on nonsmooth Riemannian manifolds ⋮ Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs ⋮ Sublinear equations driven by Hörmander operators ⋮ Unnamed Item ⋮ On Global Existence and Regularity of Solutions for a Transport Problem Related to Charged Particles ⋮ Hilbert Space Methods in the Theory of Harmonic Integrals ⋮ Définition d'opérateurs maximaux et applications ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the limiting behaviour of some nonlocal seminorms: a new phenomenon ⋮ On tamed almost complex four-manifolds ⋮ A Rademacher type theorem for Hamiltonians \(H(x, p)\) and an application to absolute minimizers ⋮ On the Nonidentity of Weak and Strong Extensions of Differential Operators ⋮ On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves ⋮ From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence ⋮ A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation ⋮ A spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation condition ⋮ Computing with a Canonical Neural Circuits Model with Pool Normalization and Modulating Feedback ⋮ On approximative linear Boltzmann transport equation for charged particles ⋮ Generalized solutions to the cubic Schrödinger equation ⋮ Identifying an unknown source term in a heat equation with time-dependent coefficients ⋮ The Identity of Weak and Strong Extensions of Pseudo-Differential Operators ⋮ k-Misure su una varietà differenziabile ⋮ Sub-Finsler Geometry and Finite Propagation Speed ⋮ Abstract Evolution Equations and the Mixed Problem for Symmetric Hyperbolic Systems ⋮ On the Cauchy problem for the elliptic complexes in spaces of distributions ⋮ Weak Equals Strong for First-Order Linear Pseudodifferential Boundary Value Problems ⋮ On the Cauchy problem for operators with injective symbols in the spaces of distributions ⋮ Unnamed Item ⋮ A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization ⋮ Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds ⋮ Variational Analysis for the Black and Scholes Equation with Stochastic Volatility ⋮ Theory of Hyperbolic Evolution Equations and Partial Differential Equations ⋮ A finite element approximation for a class of degenerate elliptic equations ⋮ A new method of extension of local maps of Banach spaces. Applications and examples ⋮ The Dirac Operator on Spaces with Conical Singularities and Positive Scalar Curvatures ⋮ On the Existence and Boundedness of Solutions of Nonlinear Partial Differential Equations of Parabolic Type