Seventy five (thousand) unsolved problems in analysis and partial differential equations

DOI10.1007/s00020-018-2460-8zbMath1398.35019OpenAlexW2801721719MaRDI QIDQ1637336

Vladimir Gilelevich Maz'ya

Publication date: 8 June 2018

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-018-2460-8

zbMATH Keywords

Sobolev spacesintegral operatorshyperbolic operatorsStokes and Navier-Stokes systemslinear and nonlinear elliptic operatorsparablic operators

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Integral equations (45-XX) Research exposition (monographs, survey articles) pertaining to integral equations (45-02) Parabolic equations and parabolic systems (35Kxx) Hyperbolic equations and hyperbolic systems (35Lxx) Linear function spaces and their duals (46Exx) Elliptic equations and elliptic systems (35Jxx)

Related Items

Sharp second order uncertainty principles ⋮ A survey of functional and Lp-dissipativity theory ⋮ An optimal Sobolev embedding for \(L^1\) ⋮ Strong Singularities of Solutions to Nonlinear Elliptic Equations ⋮ Positive Liouville theorem and asymptotic behaviour for (p, A)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space ⋮ Asymptotic behavior of 𝐿^{𝑝} estimates for a class of multipliers with homogeneous unimodular symbols ⋮ Sharp uncertainty principle inequality for solenoidal fields ⋮ The Stokes resolvent problem: optimal pressure estimates and remarks on resolvent estimates in convex domains ⋮ Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives ⋮ Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space ⋮ Uniqueness and bifurcation branches for planar steady Navier-Stokes equations under Navier boundary conditions ⋮ Eight(y) mathematical questions on fluids and structures ⋮ \(p\)-Bessel pairs, Hardy's identities and inequalities and Hardy-Sobolev inequalities with monomial weights ⋮ Uncertainty Type Principles for Radial Derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and regularity of positive solutions of elliptic equations of Schrödinger type
• \(L^p\) solvability of the stationary Stokes problem in domains with conical singularity in any dimension
• Notes on Hölder regularity of a boundary point with respect to an elliptic operator of second order
• Function spaces as Dirichlet spaces (about a paper by Maz'ya and Nagel)
• Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak
• Extremal length and functional completion
• Estimates for differential operators of vecor analysis involving \(L^{1}\)-norm
• A Wiener-type condition for Hölder continuity for Green's functions
• A new type of integral equations related to the co-area formula (reduction of dimension in multi-dimensional integral equations)
• Pointwise inequalities for elliptic boundary value problems
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium
• Sharp Hardy-Leray inequality for axisymmetric divergence-free fields
• On representation of the solution of the Neumann problem in a domain with peak by the harmonic simple layer potential
• The vertex of a cone can be nonregular in the Wiener sense for a fourth- order elliptic equation
• Approximation of Sobolev functions in Jordan domains
• Spectral properties of the operator bundles generated by elliptic boundary-value problems in a cone
• Removable singularities of bounded solutions of quasilinear elliptic equations of any order
• Index of the closure of the operator of the Dirichlet problem in a domain with an irregular boundary
• Some counterexamples for the theory of Sobolev spaces on bad domains
• Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
• Invariant convex bodies for strongly elliptic systems
• On certain integral inequalities for functions of many variables
• The Wiener test for higher order elliptic equations.
• Quasilinear elliptic equations and weighted Sobolev-Poincaré inequalities with distributional weights
• On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik boundary point principle
• On solvability of boundary integral equations of potential theory for a multidimensional cusp domain
• Resolvent estimates in \(L ^{p }\) for the Stokes operator in Lipschitz domains
• Semi-bounded differential operators, contractive semigroups and beyond
• Asymptotic formula for solutions to elliptic equations near the Lipschitz boundary
• A discontinuous solution of a mildly nonlinear elliptic system
• Can one see the fundamental frequency of a drum?
• A remark on the characteristic Cauchy problem
• The global Goursat problem and scattering for nonlinear wave equations
• Sets of uniqueness for functions regular in the unit circle
• On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points
• Sur la complétion par rapport à une intégrale de Dirichlet
• Parabolic Capacity and Sobolev Spaces
• Theory of Sobolev Multipliers
• A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions
• On The Dirichletproblem for Quasilinear Equations
• The Integrability of the Derivative in Conformal Mapping
• Index Formulas for Elliptic Boundary Value Problems in Plane Domains with Corners
• On Certain Hybrid Iterative Methods for Solving Boundary Value Problems
• Solvability of the two-dimensional kelvin-neumann problem for a submerged circular cylinder
• Linear Water Waves
• Geometry and stability of bubbles with gravity
• USE OF (p,l)-CAPACITY IN PROBLEMS OF THE THEORY OF EXCEPTIONAL SETS
• On the spectrum of general second order operators
• The Fredholm Method in Potential Theory
• Sobolev Spaces
• On the Unboundedness of the Essential Spectrum