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Nonlinear Analysis, ISSN 0362-546X, 10/2019, Volume 187, pp. 339 - 351
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2019, Volume 88, Issue 315, pp. 179 - 210
We develop finite element exterior calculus over weakly Lipschitz domains. Specifically, we construct commuting projections from L^p de Rham complexes over... 
Lipschitz collar | Smoothed projection | Finite element exterior calculus | Geometric measure theory | Weakly Lipschitz domain | HODGE DECOMPOSITIONS | MATHEMATICS, APPLIED | geometric measure theory | SPACES | weakly Lipschitz domain | STABILITY | EQUATIONS | ELEMENT EXTERIOR CALCULUS | FINITE | DIFFERENTIAL FORMS | smoothed projection | MANIFOLDS
Journal Article
INVERSE PROBLEMS, ISSN 0266-5611, 05/2019, Volume 35, Issue 5, p. 54005
Compton scatter tomography (CST) is an imaging process which reconstructs the electric charge density in a two-dimensional slice of an object. We describe a... 
EXTERIOR | MATHEMATICS, APPLIED | imaging science integral geometry | RADON-TRANSFORM | RECONSTRUCTION | generalized Radon transforms | Compton scatter tomography | INVERSION | PHYSICS, MATHEMATICAL
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 01/2016, Volume 130, pp. 241 - 254
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 1/2015, Volume 52, Issue 1, pp. 39 - 63
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2016, Volume 307, pp. 248 - 261
Riemann–Hilbert problems in multiply connected domains arise in a number of applications, such as the computation of conformal maps. As an example here, we... 
Multiply connected domains | Conformal mapping | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Riemann-Hilbert problems | Linear systems | Maps | Computation | Exteriors | Disks | Mathematical models | Slits | Inclination
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2010, Volume 265, Issue 2, pp. 297 - 320
We study integral operators related to a regularized version of the classical Poincare path integral and the adjoint class generalizing Bogovskii's integral... 
Differential forms | Lipschitz domain | Pseudodifferential operator | Sobolev spaces | Exterior derivative | MATHEMATICS | SPACES | NONSMOOTH | EQUATION | Analysis of PDEs | Numerical Analysis | Mathematics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2016, Volume 260, Issue 11, pp. 8025 - 8050
In this article we are interested in the existence of positive classical solutions of(1){−Δu+a(x)⋅∇u+V(x)u=up+γuq in Ωu=0 on ∂Ω,... 
Nonlinear gradient | Linearized operators | Entire solutions | Lane–Emden | Exterior domains | MATHEMATICS | LOCAL BEHAVIOR | CLASSIFICATION | ELLIPTIC-EQUATIONS | Lane-Emden
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2019, Volume 469, Issue 1, pp. 188 - 201
We obtain the critical exponent for the Dirichlet exterior problemiut+Δu=λ|u|p,in(0,∞)×Dc,u(t,x)=f(x),in(0,∞)×∂D,u(0,x)=g(x),inDc, where u is a complex valued... 
Exterior domain | Critical exponent | Schrödinger equation | MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger equation | NONEXISTENCE | BLOW-UP | GLOBAL-SOLUTIONS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2020
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 09/2018, Volume 174, pp. 17 - 53
We investigate the Fredholm alternative for the p-Laplacian in an exterior domain which is the complement of the closed unit ball in RN (N≥2). By employing... 
Fredholm alternative | Variational method | Exterior domain | [formula omitted]-Laplacian | The first eigenvalue | p-Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | OPERATOR | 1ST EIGENVALUE | ELLIPTIC-EQUATIONS | PRINCIPAL EIGENVALUE
Journal Article
Positivity, ISSN 1385-1292, 11/2019, Volume 23, Issue 5, pp. 1147 - 1164
We study a nonlinear eigenvalue problem on the exterior to a simply connected bounded domain in $$\mathbb {R}^N$$ R N containing the origin. We consider... 
Positive weak solution | Mathematics | Primary 35J60 | Secondary 35J75 | Singular problem | S -shaped bifurcation diagram | 35J66 | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Exterior domain | Decay | Econometrics | S-shaped bifurcation diagram | EIGENVALUE | CRITERIA | MATHEMATICS | UNIQUENESS
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 02/2018, Volume 124, pp. 22 - 43
In this paper, we consider 3D wave propagation problems in unbounded domains, such as those of acoustic waves in non viscous fluids, or of seismic waves in... 
Exterior wave propagation problems | Space–time boundary integral equations | Non reflecting boundary conditions | Numerical methods | EXTERIOR | DIMENSIONS | MATHEMATICS, APPLIED | CONVOLUTION QUADRATURE | Space-time boundary integral equations | BIE METHOD | Seismic waves | Wave propagation
Journal Article
St. Petersburg Mathematical Journal, ISSN 1061-0022, 04/2019, Volume 30, Issue 2, pp. 161 - 179
Analogs of Hardy-Rellich inequalities are studied for compactly supported functions on the domains of Euclidean space in the case when weight functions are... 
MATHEMATICS | Rellich inequality | Hardy inequality | CONSTANTS | nonconvex domain | exterior sphere condition
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2020, Volume 361, p. 106927
We establish quadratic asymptotics for solutions to special Lagrangian equations with supercritical phases or with semiconvexity on solutions in exterior... 
Monge-Ampère type equations | Exterior Bernstein-Liouville problem | Special Lagrangian equation | MATHEMATICS | Monge-Ampere type equations | BEHAVIOR | EXTENSION | ELLIPTIC-EQUATIONS | LIOUVILLE-TYPE THEOREM | UNIQUENESS | SURFACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2015, Volume 427, Issue 2, pp. 856 - 872
The purpose of this paper is to investigate positive solutions of integral equations involving Riesz potential. Exploiting the moving plane method in integral... 
The method of moving planes | Integral equations involving Riesz potential | Symmetry of domains and solutions | Exterior and annular domains | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | BALLS | REGULARITY | SYSTEMS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2020, Volume 485, Issue 1, p. 123776
In this paper, we prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear elliptic equations F(D2u,Du,u,x)=0 and fully nonlinear... 
Radial symmetry | Annular domains | Viscosity solutions | Exterior domains | Moving plane method
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 1, pp. 22 - 43
In the paper, we consider the Hessian equation σk(λ(D2u))=f(x) where f is a positive function outside a bounded domain of Rn, n≥3 and f(x)=1+O(|x|−β) for some... 
Exterior Dirichlet problem | Generalized symmetric function | k-Hessian equation | Existence | Perron's method | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | UNIQUENESS | MATHEMATICS | 2ND-ORDER ELLIPTIC-EQUATIONS | REGULARITY | DIRICHLET PROBLEM | MONGE-AMPERE EQUATION
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2014, Volume 109, pp. 148 - 155
We prove the existence of a solution between an ordered pair of sub and supersolutions for singular quasilinear elliptic problems on unbounded domains.... 
Unbounded domains | Infinite semipositone | Singular problems | [formula omitted]-Laplacian | Sub and supersolutions | p-Laplacian | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | NONLINEARITIES | INFINITE SEMIPOSITONE PROBLEMS | MATHEMATICS | EXTERIOR DOMAINS | REGULARITY | DIRICHLET-PROBLEM | Origins | Texts | Nonlinearity | Radon | Decay
Journal Article
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