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Inverse Problems, ISSN 0266-5611, 01/2019, Volume 35, Issue 3, p. 35004
The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed... 
nonlinear quasi-variational inequality | obstacle problem | p -Laplacian | inverse problems | regularization | EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | HEMIVARIATIONAL INEQUALITIES | IDENTIFICATION | PHYSICS, MATHEMATICAL | VALUED EQUILIBRIUM PROBLEMS
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2011, Volume 42, Issue 1, pp. 21 - 41
Journal Article
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2020, Volume 193, p. 111459
We study a model for combustion on a boundary. Specifically, we study certain generalized solutions of the equation (−Δ)su=χ{u>c}for 0 Free boundary | Unstable | Obstacle problem | MATHEMATICS | MATHEMATICS, APPLIED | EXTENSION PROBLEM | Upper bounds | Free boundaries
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 12/2016, Volume 41, Issue 12, pp. 1918 - 1933
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 11/2017, Volume 273, Issue 10, pp. 3061 - 3093
We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff... 
Porous medium equation | Free boundary problems | Tumor growth | Hele–Shaw equation | OBSTACLE PROBLEM | MATHEMATICS | POROUS-MEDIUM EQUATION | REGULARITY | Hele-Shaw equation | MEDIA EQUATION | BOUNDARY | FLOW | Analysis | Tumors | Analysis of PDEs | Mathematics
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 10/2010, Volume 35, Issue 11, pp. 2092 - 2122
The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type... 
35J10 | 35B05 | 35J70 | 26A33 | 35K05 | Degenerate Schrödinger equation | Heat semigroup | Fractional Laplacian | Harnack's inequality | Harmonic oscillator | Degenerate schrödinger equation | Fractional laplacian | OBSTACLE PROBLEM | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | Degenerate Schrodinger equation | Partial differential equations | Inequality
Journal Article
Acta Numerica, ISSN 0962-4929, 05/2012, Volume 21, pp. 89 - 305
In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary... 
MATHEMATICS | Boundary conditions | Acoustics | Numerical analysis | Asymptotic methods | Scattering | Design engineering | Obstacles | Construction | Asymptotic properties | Integrals | Boundary integral method | Mathematical models
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 11/2018, Volume 85, pp. 125 - 131
This work aims at studying the virtual element method (VEM) to solve a simplified friction problem, which is a typical elliptic variational inequality of the... 
Polygonal meshes | Variational inequality | Optimal error estimate | VARIATIONAL-INEQUALITIES | MATHEMATICS, APPLIED | APPROXIMATION | OBSTACLE PROBLEMS | DISCONTINUOUS GALERKIN METHODS | FORMULATION
Journal Article
Inverse Problems, ISSN 0266-5611, 09/2015, Volume 31, Issue 9, pp. 93001 - 93021
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2020, Volume 269, Issue 1, pp. 542 - 562
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 12/2018, Volume 177, pp. 699 - 732
We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order s∈(0,1) and summability... 
Integro-differential operators | Nonlocal tail | Fractional Sobolev spaces | OBSTACLE PROBLEM | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | HOLDER CONTINUITY | SUPERHARMONIC FUNCTIONS | PARABOLIC EQUATIONS | INTEGRODIFFERENTIAL OPERATORS | NONLOCAL EQUATIONS | ZYGMUND THEORY | MATHEMATICS | NONLINEAR EQUATIONS | ELLIPTIC-EQUATIONS | Analysis | Differential equations
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 06/2015, Volume 120, pp. 107 - 117
We consider a system of an evolutionary variational inequality of two obstacles type, depending on the temperature, coupled with the heat equation. We prove... 
Variational inequality | Two obstacles | Coupled problem | MATHEMATICS | MATHEMATICS, APPLIED | Obstacles | Nonlinearity | Joining | Evolutionary | Inequalities | Heat equations
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2018, Volume 50, Issue 1, pp. 119 - 137
We consider an obstacle problem for elastic curves given by graphs with fixed ends. We give conditions on the obstacles that assure existence of solutions and... 
Fourth order | Regularity | Elastic energy | Obstacle problem | fourth order | MATHEMATICS, APPLIED | obstacle problem | regularity | elastic energy
Journal Article
Inverse Problems, ISSN 0266-5611, 07/2018, Volume 34, Issue 10, p. 105001
In this paper we study shape derivatives of solutions of acoustic and electromagnetic scattering problems in frequency domain from the perspective of... 
differential forms | acoustic scattering | shape derivative | shape calculus | electromagnetic scattering | INTERFACE PROBLEMS | MATHEMATICS, APPLIED | INVERSE SCATTERING | DIFFERENTIABILITY | PHYSICS, MATHEMATICAL | OBSTACLE SCATTERING | IMPEDANCE | BOUNDARY INTEGRAL-OPERATORS | 2ND MOMENT ANALYSIS
Journal Article
Mathematics and Mechanics of Solids, ISSN 1081-2865, 5/2019, Volume 24, Issue 5, pp. 1503 - 1529
Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement... 
asymptotic analysis | Obstacle problems | variational inequalities | elliptic membrane shells | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MATERIALS SCIENCE, MULTIDISCIPLINARY | MATHEMATICAL JUSTIFICATION | Mathematical Physics | Analysis of PDEs | Mathematics
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 2, pp. A918 - A945
Journal Article
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